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arXiv · 1509.00178

A variational method for second order shape derivatives

Guy Bouchitté·Ilaria Fragalà·Ilaria Lucardesi
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Abstract

We consider shape functionals obtained as minima on Sobolev spaces of classical integrals having smooth and convex densities, under mixed Dirichlet-Neumann boundary conditions. We propose a new approach for the computation of the second order shape derivative of such functionals, yielding a general existence and representation theorem. In particular, we consider the p-torsional rigidity functional for p grater than or equal to 2.

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Guy Bouchitté, Ilaria Fragalà, Ilaria Lucardesi. 2015-09-01. A variational method for second order shape derivatives. https://doi.org/10.1137/15100494x

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