Some optimization problems for p-Laplacian type equations

Abstract

In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem of optimizing the cost functional J (u) = ∂ f (x)u dHN−1 over some admissible class of loads f where u is the (unique) solution to the problem −Δ p u+|u|p−2 u=0 in Ω with |∇ u|p−2 u ν =f on ∂Ω.