PDE Seminar Abstracts

Minimal Solution to Some Variational Inequalities

Michel Chipot
Universit├Ąt Z├╝rich, 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

u K : Au,v - uΩf(v - udx)for all v K

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 v W01,p(Ω) and f Lq(Ω) where q is the conjugate of p.

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