PDE Seminar: abstract

Abstract

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 : ⟨ A u, v - u ⟩ \geq \int_{Ω} f (v - u d x) for all v \in K

where $Ω$ is a domain in $ℝ^{n}$ , $K$ is a closed convex subset of $W_{0}^{1, p} (Ω)$ , $A$ is a nonlinear operator defined from $W_{0}^{1, p} (Ω)$ into its dual by

⟨ A u, v ⟩ = \int_{Ω} a (x, u, \nabla u) \cdot \nabla v d x + \int_{Ω} a_{0} (x, u, \nabla u) v d x

for all $v \in W_{0}^{1, p} (Ω)$ and $f \in L^{q} (Ω)$ where $q$ is the conjugate of $p$ .

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

Minimal Solution to Some Variational Inequalities

Abstract