Some optimization problems for nonlinear elastic membranes

Details Some optimization problems for nonlinear elastic membranes Some optimization problems for nonlinear elastic membranes

2008-01-14

arxiv.org/abs/0801.2085v2

Mathematics

Analysis of PDEs

New version with corrections made by the referee

Scientific paper

In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem of optimizing the cost functional $\J(u)=\int_{\partial\Omega} f(x) u \rd \H^{N-1}$ over some admissible class of loads $f$ where $u$ is the (unique) solution to the problem $-\Delta_p u + |u|^{p-2}u = 0$ in $\Omega$ with $|\nabla u|^{p-2}u_\nu = f$ on $\partial \Omega$.

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