PDE Real Analysis Seminar

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

Date, time & place Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.)

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