Il 18 Aprile alle ore 14.30 nella sala Professori al I livello il prof. Luca Esposito terrà un seminario dal titolo

REGULARITY RESULTS FOR OPTIMAL DESIGN PROBLEMS INVOLVING BOTH BULK AND SURFACE ENERGIES.

Abstract. This presentation discusses some regularity results concerning an optimal design problem, which have been achieved through collaboration with Lorenzo Lamberti. We study a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type albeit of very general form allowing the dependence from the unknown variable u and the position x. We employ the regularity theory of Λ-minimizers to study the regularity of the free interface. The hallmark of the paper is the mild regularity assumption concerning the dependence of the coefficients with respect to x and u that is of H ̈older type.