PDE Seminar Abstracts

Michel Chipot

Universität Zürich, Switzerland

Fri 18th Nov 2016, 11-12am, Carslaw Lecture Theater 157

Universität Zürich, Switzerland

Fri 18th Nov 2016, 11-12am, Carslaw Lecture Theater 157

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

$$u\in K:\u27e8Au,v-u\u27e9\ge {\int}_{\Omega}f\left(v-udx\right)\phantom{\rule{1em}{0ex}}\text{forall}v\in K\text{}$$

where $\Omega $ is a domain in ${\mathbb{R}}^{n}$, $K$ is a closed convex subset of ${W}_{0}^{1,p}\left(\Omega \right)$, $A$ is a nonlinear operator defined from ${W}_{0}^{1,p}\left(\Omega \right)$ into its dual by

$$\u27e8Au,v\u27e9={\int}_{\Omega}a\left(x,u,\nabla u\right)\cdot \nabla v\phantom{\rule{0.3em}{0ex}}dx+{\int}_{\Omega}{a}_{0}\left(x,u,\nabla u\right)v\phantom{\rule{0.3em}{0ex}}dx$$

for all $v\in {W}_{0}^{1,p}\left(\Omega \right)$ and $f\in {L}^{q}\left(\Omega \right)$ where $q$ is the conjugate of $p$.

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

Back to Seminar Front Page