PDE Real Analysis Seminar

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Seminar information archive ～06/27｜Next seminar｜Future seminars 06/28～

Date, time & place	Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.)
Organizer(s)	Yoshikazu Giga, Kazuhiro Ishige, Hiroyoshi Mitake, Tsuyoshi Yoneda
URL	https://www.math.sci.hokudai.ac.jp/coe/sympo/pde_ra/index_en.html

2005/05/25

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Vincenzo Vespri (Dipartimento di Matematica Ulisse Dini Viale Morgagni) 10:30-11:30
Some regularity results for Stefan equation

[ Abstract ]
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.

[ Reference URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Paolo Marcellini (Università degli Studi di Firenze) 11:45-12:45
Nonlinear elliptic systems with general growth

[ Abstract ]
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.

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

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