Some optimization problems for nonlinear elastic membranes

2008/01/14 by L. Del Pezzo, Del Pezzo, L., J. Fernandez Bonder +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.0801.2085

New version with corrections made by the referee

arxiv created 2008/06/12 · arxiv updated 2009/12/01

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)=∫_∂Ω f(x) u \rd \H^N-1 over some admissible class of loads f where u is the (unique) solution to the problem -Δ_p u + |u|^p-2u = 0 in Ω with |∇ u|^p-2u_ν= f on ∂ Ω.

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