Some Optimization Problems for p-Laplacian Type Equations.

In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem of optimizing the cost functional $\mathcal {J}(u)=\int_{\partial\Omega}f(x)u\,\mathrm {d}\mathcal {H}^{N-1}$ 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. [ABSTRACT FROM AUTHOR]