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.
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Supported by Universidad de Buenos Aires under grant X078, by ANPCyT PICT No. 2006-290 and CONICET (Argentina) PIP 5478/1438.
J. Fernández Bonder is a member of CONICET. Leandro M. Del Pezzo is a fellow of CONICET.
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Del Pezzo, L.M., Fernández Bonder, J. Some Optimization Problems for p-Laplacian Type Equations. Appl Math Optim 59, 365–381 (2009). https://doi.org/10.1007/s00245-008-9058-5
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DOI: https://doi.org/10.1007/s00245-008-9058-5