Shape derivatives for minima of integral functionals

A Variational Method for Second Order Shape Derivatives

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 functio...

On the Symmetry of Second Derivatives in Optimal Shape Design and Suucient Optimality Conditions for Shape Functionals

For some heuristic approaches of the boundary variation in shape optimization the computation of second derivatives of domain and boundary integral functionals, their symmetry and a comparison to the velocity eld or material derivative method are discussed. Moreover, for some of these approaches the funcionals are Fr echet-diierentiable, because an embedding into a Banach space problem is possi...

A Derivation Formula for Convex Integral Functionals Deened on Bv ()

We show that convex lower semicontinuous functionals deened on functions of bounded variation are characterized by their minima, and we prove a derivation formula which allows an integral representation of such functionals. Applications to relaxation and homogenization are given.

Minima of Non Coercive Functionals

In this paper we study a class of integral functionals defined on H 0 (Ω), but non coercive on the same space, so that the standard approach of the Calculus of Variations does not work. However, the functionals are coercive on W 1,1 0 (Ω) and we will prove the existence of minima, despite the non reflexivity of W 1,1 0 (Ω), which implies that, in general, the Direct Methods fail due to lack of ...

A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces