Some Optimization Problems for p-Laplacian Type Equations

Article

DOI: 10.1007/s00245-008-9058-5

Cite this article as:
Del Pezzo, L.M. & Fernández Bonder, J. Appl Math Optim (2009) 59: 365. doi:10.1007/s00245-008-9058-5

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 −Δpu+|u|p−2u=0 in Ω with |u|p−2uν=f on Ω.

Keywords

Shape derivativeLoad optimizationp-Laplace equation

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Departamento de Matemática, FCEyNUniversidad de Buenos AiresBuenos AiresArgentina