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PDE Seminar Abstracts

PDE’s involving variable exponents

Mihai Mihăilescu
University of Craiova, Romania
Mon 3 September 2012 2-3pm, AGR Carslaw 829

Abstract

We discuss some aspects regarding the eigenvalue problem -Δp(x)u=λ|u|p(x)-2u if xΩ, u=0 if xΩ, where ΩRN is a bounded domain, p:ˉΩ(1,) is a continuous function and Δp(x)u:=(|u|p(x)-2u) stands for the p(x)-Laplace operator. Let Λ be the set of eigenvalues of the above problem and λ*=inf. In particular, we will emphasize, on the one hand, situations when λ* vanishes, and, on the other hand, we will advance some sufficient conditions when λ* is positive. In the case when p C1(Ω) some extensions will be presented. In a related context some connections with a maximum principle will be pointed out.