Calculus of Variations and Geometric Measure Theory

G. Bouchitté - I. Fragalà - I. Lucardesi

A variational method for second order shape derivatives

created by lucardesi on 10 Aug 2018


Published Paper

Inserted: 10 aug 2018
Last Updated: 10 aug 2018

Journal: SIAM J. Control Optim.
Volume: 54
Number: 2
Pages: 1056–1084
Year: 2016
Doi: 10.1137/15100494X


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 $p \geq 2$.