The 11th : PDE Real Analysis Seminar

Organizers :: H.Arai (University of Tokyo) Y.Giga (University of Tokyo/Hokkaido University)
Board Members :: H.Ishii (Waseda.U) T.Kawazoe (Keio.U) N.Kenmochi (Chiba.U) M.Sakai (Tokyo Metropolitan.U) Y.Shibata (Waseda.U) K.Mochizuki (Chuo.U) A.Miyachi(Tokyo Woman's Christian.U) M.Yamazaki (Waseda.U)

Place :: Graduate School of Mathematical Sciences the University of Tokyo, Room #056

Programme :

Vincenzo Vespri (Dipartimento di Matematica Ulisse Dini Viale Morgagni): "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.

Paolo Marcellini (Università degli Studi di Firenze): "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.

The 11th PDE Real Analysis Seminar