## 過去の記録

### 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

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.
[ 講演参考URL ]
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

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
[ 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.
[ 講演参考URL ]
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

### 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
[ 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.
[ 講演参考URL ]
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.
[ 講演参考URL ]
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

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

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.
[ 講演参考URL ]
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

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

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

### 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

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.
[ 講演参考URL ]
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

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
[ 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.
[ 講演参考URL ]
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
[ 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.
[ 講演参考URL ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2005年01月26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
Matthias Hieber 氏 (ダルムシュタット工科大学)
L^p-Theory of the Navier-Stokes flow past rotating or moving obstacles
[ 講演概要 ]
In this talk we consider the equation of Navier-Stokes in the exterior of a rotating or moving domain. Using techniques from the analysis of Ornstein-Uhlenbeck operators it is shown that, after rewriting the problem on a fixed domain $\\Omega$, the solution of the linearized equation is governed by a $C_0$-semigroup on $L^p_\\sigma(\\Omega)$ for \$1 [ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2005年01月24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

Hausdorff measure and exceptional sets in Dirichlet space theory on local fields

### 2005年01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

[ 講演概要 ]

### 2004年12月17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) 126号室
D. Popovici 氏 (Warwick)
A simple proof of a theorem by Uhlenbeck and Yau

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 126号室
Min Ru 氏 (Houston)
Holomorphic curves into algebraic varieties

### 2004年12月15日(水)

#### PDE実解析研究会

10:30-12:45   数理科学研究科棟(駒場) 122号室
Andrzej Swiech 氏 (ジョージア工科大学) 10:30-11:30
Hamilton-Jacobi-Bellman equations for optimal control of stochastic Navier-Stokes equations.
[ 講演概要 ]
We consider a parameterized family of continuous functions, which containsas its members Bourbai's and Perkins's nowhere differentiable functions as well as the Cantor-Lebesgue singular functions.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Francesca Da Lio 氏 (Dipartimento di Matematica P. e A.Universit di Padova researcher) 11:45-12:45
A GEOMETRICAL APPROACH TO FRONT PROPAGATION PROBLEMS IN BOUNDED DOMAINS WITH NEUMANN-TYPE BOUNDARY AND APPLICATIONS
[ 講演概要 ]
We talk about a new definition of weak solution for the global-in-time motion of a front in bounded domains with normal velocity depending not only on its curvature but also on the measure of the set it encloses and with a contact angle boundary condition. We apply this definition to study the asymptotic behaviour of the solutions of some local and nonlocal reaction-diffusion equations.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2004年12月13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) 126号室

### 2004年12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) 122号室

A remark on continuous, nowhere differentiable functions
[ 講演概要 ]
We consider a parameterized family of continuous functions, which containsas its members Bourbai's and Perkins's nowhere differentiable functions as well as the Cantor-Lebesgue singular functions.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2004年10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) 122号室
Hermann Sohr 氏 (University of Paderborn)
Some recent results on the Navier-Stokes equations
[ 講演概要 ]
The aim of this talk is to explain some new results in particular on local regularity properties of Hopf type weak solutions to the Navier-Stokes equations for arbitrary domains. Further we explain a new existence result for nonhomogeneous data and a result for global regular solutions with "slightly" modified forces.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2004年10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) 128号室
Philippe G. LeFloch 氏 (University of Paris 6)
Existence, uniqueness, and continuous dependence of entropy solutions to hyperbolic systems
[ 講演概要 ]
I will review the well-posedness theory of nonlinear hyperbolic systems, in conservative or in non-conservative form, by focusing attention on the existence and properties of entropy solutions with sufficiently small total variation.
New results and perspectives on the following issues will be discussed: Glimm's existence theorem,

Bressan-LeFloch's uniqueness theorem,and the L1 continuous dependence property (established by Bressan, LeFloch, Liu, and Yang).
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2004年09月29日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 117号室
Alex Mahalov 氏 (Arizona State University)
Global Regularity of the 3D Navier-Stokes with Uniformly Large Initial Vorticity
[ 講演概要 ]
We prove existence on infinite time intervals of regular solutions to the 3D Navier-Stokes Equations for fully three-dimensional initial data characterized by uniformly large vorticity with periodic boundary conditions and in bounded cylindrical domains; smoothness assumptions for initial data are the same as in local existence theorems. There are no conditional assumptions on the properties of solutions at later times, nor are the global solutions close to any 2D manifold.
The global existence is proven using techniques of fast singular oscillating limits and the Littlewood-Paley dyadic decomposition. The approach is based on the computation of singular limits of rapidly oscillating operators and cancellation of oscillations in the nonlinear interactions for the vorticity field. With nonlinear averaging methods in the context of almost periodic functions, we obtain fully 3D limit resonant Navier-Stokes equations. Using Lemmas on restricted convolutions, we establish the global regularity of the latter without any restriction on the size of 3D initial data.
With strong convergence theorems, we bootstrap this into the global regularity of the 3D Navier-Stokes Equations with uniformly large initial vorticity.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html