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過去の記録
過去の記録 ～01/15｜本日 01/16 | 今後の予定 01/17～
2005年10月17日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
吉川謙一 氏 (東大数理)
On the discriminant of certain K3 surfaces
吉川謙一 氏 (東大数理)
On the discriminant of certain K3 surfaces
2005年09月28日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Matthias Geissert 氏 (ダルムシュタット工科大学)
The Navier-Stokes flow in the exterior of a rotating obstacle
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Matthias Geissert 氏 (ダルムシュタット工科大学)
The Navier-Stokes flow in the exterior of a rotating obstacle
[ 講演概要 ]
We show the existence of solutions of the Navier-Stokes flow in the exterior of a rotating obstacle. In the first step we transform the Navier-Stokes equations to a problem in a time independent domain. In this talk we present two different change of coordinates to do this. Finally, we discuss the advantages of both approaches and show the local existence and uniqueness of mild and strong $L^p$ solutions.
[ 参考URL ]We show the existence of solutions of the Navier-Stokes flow in the exterior of a rotating obstacle. In the first step we transform the Navier-Stokes equations to a problem in a time independent domain. In this talk we present two different change of coordinates to do this. Finally, we discuss the advantages of both approaches and show the local existence and uniqueness of mild and strong $L^p$ solutions.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005年07月22日(金)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
倉西正武 氏 (コロンビア大学)
Szegö kernel の構成について
倉西正武 氏 (コロンビア大学)
Szegö kernel の構成について
複素解析幾何セミナー
15:30-17:00 数理科学研究科棟(駒場) 128号室
Dan Popovici 氏 (JSPS, 名古屋大学多元数理)
Effective Local Finite Generation of Multiplier Ideal Sheaves
Dan Popovici 氏 (JSPS, 名古屋大学多元数理)
Effective Local Finite Generation of Multiplier Ideal Sheaves
2005年07月20日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
相川弘明 氏 (島根大学)
Equivalence between the boundary Harnack principle and the Carleson estimate
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
相川弘明 氏 (島根大学)
Equivalence between the boundary Harnack principle and the Carleson estimate
[ 講演概要 ]
Both the boundary Harnack principle and the Carleson estimate describe the boundary behavior of positive harmonic functions vanishing on a portion of the boundary. These notions are inextricably related and have been obtained simultaneously for domains with specific geometrical conditions. The main aim of this talk is to show that the boundary Harnack principle and the Carleson estimate are equivalent for arbitrary domains.
[ 参考URL ]Both the boundary Harnack principle and the Carleson estimate describe the boundary behavior of positive harmonic functions vanishing on a portion of the boundary. These notions are inextricably related and have been obtained simultaneously for domains with specific geometrical conditions. The main aim of this talk is to show that the boundary Harnack principle and the Carleson estimate are equivalent for arbitrary domains.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005年07月13日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 122号室
Yonggeun Cho 氏 (北海道大学)
On classical solutions of the compressible Navier-Stokes equation with nonnegative density
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Yonggeun Cho 氏 (北海道大学)
On classical solutions of the compressible Navier-Stokes equation with nonnegative density
[ 講演概要 ]
In this talk, we discuss a recent progress on the regularity of solution of compressible Navier-Stokes equations with nonnegative density. The nonnegativity of density cauases a problem in using the usual parabolicity of momentum equations and hence in general makes it hard to gain a regularity of solution. To overcome the difficulty, we develop a natural compatibility condition. Then observing a smoothing effect for positive time, we obtain classical solutions of the compressible Navier-Stokes equations.
[ 参考URL ]In this talk, we discuss a recent progress on the regularity of solution of compressible Navier-Stokes equations with nonnegative density. The nonnegativity of density cauases a problem in using the usual parabolicity of momentum equations and hence in general makes it hard to gain a regularity of solution. To overcome the difficulty, we develop a natural compatibility condition. Then observing a smoothing effect for positive time, we obtain classical solutions of the compressible Navier-Stokes equations.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005年07月11日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
青柳美輝 氏 (上智大理工)
学習理論のゼータ関数と特異点解消
青柳美輝 氏 (上智大理工)
学習理論のゼータ関数と特異点解消
2005年07月04日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
辻 元 氏 (上智大理工)
Variation of Bergman kernel of projective manifolds
辻 元 氏 (上智大理工)
Variation of Bergman kernel of projective manifolds
2005年06月27日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
相原義弘 氏 (沼津高専)
Uniqueness problem of analytic coverng spaces
相原義弘 氏 (沼津高専)
Uniqueness problem of analytic coverng spaces
2005年06月22日(水)
諸分野のための数学研究会
16:30-17:30 数理科学研究科棟(駒場) 056号室
Y. H. Richard Tsai 氏 (University of Texas)
Threshold Dynamics for the Piecewise Constant
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Y. H. Richard Tsai 氏 (University of Texas)
Threshold Dynamics for the Piecewise Constant
[ 講演概要 ]
We propose an efficient algorithm for minimizing the piecewise constant Mumford-Shah functional of image segmentation. It is based on the threshold dynamics of Merriman, Bence, and Osher for evolving an interface by its mean curvature. We show that a very fast minimization can be achieved by alternating the solution of a linear parabolic partial differential equation and simple thresholding. We discuss our current work of extending this line of work to higher order accuracy and to applications involving Willmore flow.
[ 参考URL ]We propose an efficient algorithm for minimizing the piecewise constant Mumford-Shah functional of image segmentation. It is based on the threshold dynamics of Merriman, Bence, and Osher for evolving an interface by its mean curvature. We show that a very fast minimization can be achieved by alternating the solution of a linear parabolic partial differential equation and simple thresholding. We discuss our current work of extending this line of work to higher order accuracy and to applications involving Willmore flow.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
2005年06月15日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
中井英一 氏 (大阪教育大学)
Singular and fractional integral operators on function spaces related to Morrey spaces
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
中井英一 氏 (大阪教育大学)
Singular and fractional integral operators on function spaces related to Morrey spaces
[ 講演概要 ]
It is known that the Hardy-Littlewood maximal operator, singular integral operators and fractional integral operators are bounded on L^p spaces and Morrey spaces. We extend the boundedness to generalized Morrey spaces, Orlicz-Morrey spaces, etc.
[ 参考URL ]It is known that the Hardy-Littlewood maximal operator, singular integral operators and fractional integral operators are bounded on L^p spaces and Morrey spaces. We extend the boundedness to generalized Morrey spaces, Orlicz-Morrey spaces, etc.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005年06月08日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
宮地晶彦 氏 (東京女子大学)
Weighted Hardy spaces on an interval and Jacobi series
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
宮地晶彦 氏 (東京女子大学)
Weighted Hardy spaces on an interval and Jacobi series
[ 講演概要 ]
For the classical Hardy class consisting of functions holomorphic in the unit disc, the Burkholder-Gundy-Silverstein theorem gives a characterization of the class in terms of certain maximal functions. We give a variant of this theorem related to weighted Hardy spaces on the interval(0,$\\pi$) and generalized holomorphic functions efined through ultraspherical (Gegenbauer) polynomials.
[ 参考URL ]For the classical Hardy class consisting of functions holomorphic in the unit disc, the Burkholder-Gundy-Silverstein theorem gives a characterization of the class in terms of certain maximal functions. We give a variant of this theorem related to weighted Hardy spaces on the interval(0,$\\pi$) and generalized holomorphic functions efined through ultraspherical (Gegenbauer) polynomials.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005年06月06日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
大沢健夫 氏 (名大多元数理)
Application of Hartogs type extension theorems to Levi flats in Kaehler manifolds
大沢健夫 氏 (名大多元数理)
Application of Hartogs type extension theorems to Levi flats in Kaehler manifolds
2005年06月01日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Jong-Shenq-Guo 氏 (国立台湾師範大学)
Annihilation of wave fronts of a reaction-diffusion equation
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Jong-Shenq-Guo 氏 (国立台湾師範大学)
Annihilation of wave fronts of a reaction-diffusion equation
[ 講演概要 ]
We shall present some recent results on the existence and uniqueness of 2-front entire solutions of a reaction-diffusion equation. These entire solutions behave as two opposite wave fronts approaching each other from both sides of the x-axis and then annihilating in a finite time.
[ 参考URL ]We shall present some recent results on the existence and uniqueness of 2-front entire solutions of a reaction-diffusion equation. These entire solutions behave as two opposite wave fronts approaching each other from both sides of the x-axis and then annihilating in a finite time.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005年05月30日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
宮岡礼子 氏 (九大数理)
全曲率有限な完備極小曲面のガウス写像の除外値について
宮岡礼子 氏 (九大数理)
全曲率有限な完備極小曲面のガウス写像の除外値について
2005年05月25日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Vincenzo Vespri 氏 (Dipartimento di Matematica Ulisse Dini Viale Morgagni) 10:30-11:30
Some regularity results for Stefan equation
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Paolo Marcellini 氏 (Università degli Studi di Firenze) 11:45-12:45
Nonlinear elliptic systems with general growth
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Vincenzo Vespri 氏 (Dipartimento di Matematica Ulisse Dini Viale Morgagni) 10:30-11:30
Some regularity results for Stefan equation
[ 講演概要 ]
We consider the eqation $\\beta (u)_t = A(u)$ where $A$ is an elliptic operator and $\\beta$ is a maximal graph. Under suitable hypothesis on $\\beta$ and $A$ we prove the continuity of local solutions extendind some techniques introduced in the 80's.
[ 参考URL ]We consider the eqation $\\beta (u)_t = A(u)$ where $A$ is an elliptic operator and $\\beta$ is a maximal graph. Under suitable hypothesis on $\\beta$ and $A$ we prove the continuity of local solutions extendind some techniques introduced in the 80's.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Paolo Marcellini 氏 (Università degli Studi di Firenze) 11:45-12:45
Nonlinear elliptic systems with general growth
[ 講演概要 ]
We prove \\textit{local Lipschitz-continuity} and, as a consequence, $C^{k}$%\\textit{\\ and }$C^{\\infty }$\\textit{\\ regularity} of \\textit{weak} solutions $u$ for a class of \\textit{nonlinear elliptic differential systems} of the form $\\sum_{i=1}^{n}\\frac{\\partial }{\\partial x_{i}}a_{i}^{\\alpha}(Du)=0,\\;\\alpha =1,2\\dots m$. The \\textit{growth conditions} on the dependence of functions $a_{i}^{\\alpha }(\\cdot )$ on the gradient $Du$ are so mild to allow us to embrace growths between the \\textit{linear} and the \\textit{exponential} cases, and they are more general than those known in the literature.
[ 参考URL ]We prove \\textit{local Lipschitz-continuity} and, as a consequence, $C^{k}$%\\textit{\\ and }$C^{\\infty }$\\textit{\\ regularity} of \\textit{weak} solutions $u$ for a class of \\textit{nonlinear elliptic differential systems} of the form $\\sum_{i=1}^{n}\\frac{\\partial }{\\partial x_{i}}a_{i}^{\\alpha}(Du)=0,\\;\\alpha =1,2\\dots m$. The \\textit{growth conditions} on the dependence of functions $a_{i}^{\\alpha }(\\cdot )$ on the gradient $Du$ are so mild to allow us to embrace growths between the \\textit{linear} and the \\textit{exponential} cases, and they are more general than those known in the literature.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005年05月23日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
赤堀隆夫 氏 (兵庫県立大物質理学)
A-branes from CR-geometry
赤堀隆夫 氏 (兵庫県立大物質理学)
A-branes from CR-geometry
2005年05月18日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
剣持信幸 氏 (千葉大学)
A model of damage evolution in viscous locking material.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
剣持信幸 氏 (千葉大学)
A model of damage evolution in viscous locking material.
[ 講演概要 ]
A model problem, describing the damage evolution for instance in some composite materials, is considered. The model is a system of nonlinear PDEs, which are kinetic equations for the displacement and damage quantity in the material. They are both heavily nonlinear parabolic equations, and one of them is of degenerate type. In this talk, the existence of a global in time solution is shown with some key ideas.
[ 参考URL ]A model problem, describing the damage evolution for instance in some composite materials, is considered. The model is a system of nonlinear PDEs, which are kinetic equations for the displacement and damage quantity in the material. They are both heavily nonlinear parabolic equations, and one of them is of degenerate type. In this talk, the existence of a global in time solution is shown with some key ideas.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005年05月16日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
野口潤次郎 氏 (東大数理)
Algebraic degeneracy of holomorphic curves
野口潤次郎 氏 (東大数理)
Algebraic degeneracy of holomorphic curves
2005年05月09日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
林本厚志 氏 (長野高専)
レビ形式が退化する、あるクラスの実超曲面の定義関数について
林本厚志 氏 (長野高専)
レビ形式が退化する、あるクラスの実超曲面の定義関数について
2005年04月25日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
藤川英華 氏 (東工大情報理工)
停留的写像類群とタイヒミュラー空間への作用
藤川英華 氏 (東工大情報理工)
停留的写像類群とタイヒミュラー空間への作用
2005年04月20日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
酒井 良 氏 (都立大学)
Small modifications of quadrature domains around a cusp
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
酒井 良 氏 (都立大学)
Small modifications of quadrature domains around a cusp
[ 講演概要 ]
A flow which is produced by injection of fluid into the narrow gap between two parallel planes is called a Hele-Shaw flow. We regard the flow as an increasing family of plane domains and discuss the case that the initial domain has a cusp on the boundary. We give sufficient conditions for the cusp to be a laminar-flow point.
[ 参考URL ]A flow which is produced by injection of fluid into the narrow gap between two parallel planes is called a Hele-Shaw flow. We regard the flow as an increasing family of plane domains and discuss the case that the initial domain has a cusp on the boundary. We give sufficient conditions for the cusp to be a laminar-flow point.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005年04月18日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
厚地 淳 氏 (慶大経済)
エネルギー有限な有理形関数の除外点の個数について
厚地 淳 氏 (慶大経済)
エネルギー有限な有理形関数の除外点の個数について
2005年03月23日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 122号室
Helmut Abels 氏 (Max Planck Institute)
Pseudodifferential Boundary Value Problems with Non-Smooth Coefficients
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Helmut Abels 氏 (Max Planck Institute)
Pseudodifferential Boundary Value Problems with Non-Smooth Coefficients
[ 講演概要 ]
We discuss an operator class that models elliptic differential boundary value problems as well as their solution operators and is closed under compositions. It was introduced by Boutet de Monvel in 1971 and provides a powerful tool to calculate with symbols associated to these operators. But the standard calculus and most of its further developments require that the symbols have smooth coefficient in the space and phase variable. We present some results which extend the calculus to symbols which have limited smoothness in the space variable. Such an extension is nescessary to apply the calculus to nonlinear partial differential boundary value problems and free boundary value problems.
[ 参考URL ]We discuss an operator class that models elliptic differential boundary value problems as well as their solution operators and is closed under compositions. It was introduced by Boutet de Monvel in 1971 and provides a powerful tool to calculate with symbols associated to these operators. But the standard calculus and most of its further developments require that the symbols have smooth coefficient in the space and phase variable. We present some results which extend the calculus to symbols which have limited smoothness in the space variable. Such an extension is nescessary to apply the calculus to nonlinear partial differential boundary value problems and free boundary value problems.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005年03月02日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 270号室
Italo Capuzzo-Dolcetta 氏 (Universita di Roma) 10:30-11:30
The maximum principle in unbounded domains
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Antonio Siconolfi 氏 (Universita di Roma) 11:45-12:45
Aubry set and applications
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Italo Capuzzo-Dolcetta 氏 (Universita di Roma) 10:30-11:30
The maximum principle in unbounded domains
[ 講演概要 ]
The issue of the talk is the validity of the Weak Maximum Principle for functions u satisfying a second-order partial differential inequality of the form
(*) F(x,u,Du,D^2u) ≧ 0
in a domain A of the n-dimensional euclidean space.
The main result presented in the lecture is that for bounded above upper semicontinuous functions verifying
(*) in the viscosity sense, the inequality u≦ 0 on the boundary ∂A is propagated in the interior of the domain itself, under suitable conditions on F and A.
These conditions include ellipticity of F, a general geometric condition on the (possibly) unbounded domain A and a joint requirement involving the spread of A and the decay of first order terms at infinity.
This result, contained in I.C.D, A.Leoni, A.Vitolo "The Alexandrov-Bakelman-Pucci weak Maximum Principle for fully nonlinear equations in unbounded domains", to appear in Comm.in PDE's, extends previous results due to X.Cabré and L.Caffarelli-X.Cabré.
In the second part of the talk we present different versions of Weak Maximum Principle, namely for solutions growing exponentially fast of (*) in narrow domains and for solutions of
(**) F(x,u,Du,D^2u) + c(x)u ≧ 0
(c changing sign) in domains of small measure.
[ 参考URL ]The issue of the talk is the validity of the Weak Maximum Principle for functions u satisfying a second-order partial differential inequality of the form
(*) F(x,u,Du,D^2u) ≧ 0
in a domain A of the n-dimensional euclidean space.
The main result presented in the lecture is that for bounded above upper semicontinuous functions verifying
(*) in the viscosity sense, the inequality u≦ 0 on the boundary ∂A is propagated in the interior of the domain itself, under suitable conditions on F and A.
These conditions include ellipticity of F, a general geometric condition on the (possibly) unbounded domain A and a joint requirement involving the spread of A and the decay of first order terms at infinity.
This result, contained in I.C.D, A.Leoni, A.Vitolo "The Alexandrov-Bakelman-Pucci weak Maximum Principle for fully nonlinear equations in unbounded domains", to appear in Comm.in PDE's, extends previous results due to X.Cabré and L.Caffarelli-X.Cabré.
In the second part of the talk we present different versions of Weak Maximum Principle, namely for solutions growing exponentially fast of (*) in narrow domains and for solutions of
(**) F(x,u,Du,D^2u) + c(x)u ≧ 0
(c changing sign) in domains of small measure.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Antonio Siconolfi 氏 (Universita di Roma) 11:45-12:45
Aubry set and applications
[ 講演概要 ]
For given Hamiltonian H(x, p) continuous and quasiconvex in the second argument, defined in Rn × Rn or on the cotangent bundle of a compact boundaryless manifold, we consider the equation
H= c
with c critical value, i.e. for which the equation admits locally Lipschitzcontinuous a.e. subsolutions, but not strict subsolutions. We show that there is a subset of the state variable space, called Aubry set and denoted by A, where the obstruction to the existence of such subsolutions is concentrated. We give a metric characterization of A, and we discuss its main properties.
They are applied to a projection problem in a Banach space, to the study of the largetime behaviour of subsolutions to a timedependent HamiltonJacobi equation, and to construct a Lyapunov function for a perturbed dynamics, under suitable stability assumptions.
[ 参考URL ]For given Hamiltonian H(x, p) continuous and quasiconvex in the second argument, defined in Rn × Rn or on the cotangent bundle of a compact boundaryless manifold, we consider the equation
H= c
with c critical value, i.e. for which the equation admits locally Lipschitzcontinuous a.e. subsolutions, but not strict subsolutions. We show that there is a subset of the state variable space, called Aubry set and denoted by A, where the obstruction to the existence of such subsolutions is concentrated. We give a metric characterization of A, and we discuss its main properties.
They are applied to a projection problem in a Banach space, to the study of the largetime behaviour of subsolutions to a timedependent HamiltonJacobi equation, and to construct a Lyapunov function for a perturbed dynamics, under suitable stability assumptions.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
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