Some optimization problems for nonlinear elastic membranes

Abstract

In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem of optimizing the cost functional $\J(u)=\int_{\partialΩ} f(x) u \rd \H^{N-1}$ over some admissible class of loads $f$ where $u$ is the (unique) solution to the problem $-{\Delta }_{p}u+|u{|}^{p-2}u=0$ in $\Omega$ with $|\nabla u{|}^{p-2}{u}_{\nu }=f$ on $\partial \Omega$.

New version with corrections made by the referee

Cited by in corpus (1)

• Remarks on an optimization problem for the $p-$Laplacian