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 ≥ 2.
A variational method for second order shape derivatives / Bouchitte G.; Fragala I.; Lucardesi I.. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - STAMPA. - 54:(2016), pp. 1056-1084. [10.1137/15100494X]
A variational method for second order shape derivatives
Lucardesi I.
2016
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 ≥ 2.
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