# 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

, Volume 59 (3) – Jun 1, 2009
17 pages

/lp/springer_journal/some-optimization-problems-for-p-laplacian-type-equations-I0bSESj380
Publisher
Springer-Verlag
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
D.O.I.
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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