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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.
Applied Mathematics and Optimization – Springer Journals
Published: Jun 1, 2009
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