CMU Campus
Center for Nonlinear Analysis
CNA Home People Seminars Publications Workshops and Conferences CNA Working Group Summer School Summer Undergraduate Institute Cooperation Positions Contact
Seminar Abstracts

Jose Miguel Urbano, Departamento de Matematicia, Universidade de Coimbra

Abstract: We study the Dirichlet problem for the p(x)-Laplacian, in the case when the variable exponent $ p(x)$ is infinite in a subdomain $ D$. The main issue is to give a proper sense to what a solution is. To this end, we consider the limit of the solutions $ u_n$ to the corresponding problem when $ p_n(x) = {\rm min} (p(x),n)$, in particular, with $ p_n=n$ in $ D$. Under suitable assumptions on the data, we find that such a limit exists and that it can be characterized as the unique solution of a variational minimization problem. Moreover, we examine this limit in the viscosity sense and find an equation it satisfies.

TUESDAY, February 3, 2009
Time: 1:30 P.M.
Location: PPB 300