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Some Optimization Problems for p -Laplacian Type Equations

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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Some Optimization Problems for p -Laplacian Type Equations

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References (19)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Springer Science+Business Media, LLC
Subject
Mathematics; Numerical and Computational Methods ; Mathematical Methods in Physics; Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-008-9058-5
Publisher site
See Article on Publisher Site

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.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jun 1, 2009

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