, Volume 59, Issue 3, pp 365-381
Date: 16 Sep 2008

Some Optimization Problems for p-Laplacian Type Equations

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Abstract

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.

Supported by Universidad de Buenos Aires under grant X078, by ANPCyT PICT No. 2006-290 and CONICET (Argentina) PIP 5478/1438.
J. Fernández Bonder is a member of CONICET. Leandro M. Del Pezzo is a fellow of CONICET.