PDE Seminar Abstracts

Minimal Solution to Some Variational Inequalities

Michel Chipot
Universität Zürich, Switzerland
Fri 18th Nov 2016, 11-12am, Carslaw Lecture Theater 157

Abstract

We would like to present some new results regarding the existence of a minimal solution to some variational inequalities of the type

uK:Au,v-uΩf(v-udx)for all vK

where Ω is a domain in n, K is a closed convex subset of W01,p(Ω), A is a nonlinear operator defined from W01,p(Ω) into its dual by

Au,v=Ωa(x,u,u)vdx+Ωa0(x,u,u)vdx

for all vW01,p(Ω) and fLq(Ω) where q is the conjugate of p.

This is joint work with S. Guesmia and S. Harkat.