Calculus of Variations and Geometric Measure Theory

G. Buttazzo

Spectral Optimization Problems

created by buttazzo on 10 Nov 2010



Inserted: 10 nov 2010

Pages: 42
Year: 2010


In this survey paper we present a class of shape optimization problems where the cost function involves the solution of a PDE of elliptic type in the unknown domain. In particular, we consider cost functions which depend on the spectrum of an elliptic operator and we focus on the existence of an optimal domain. The known results are presented as well as a list of still open problems. Related fields as optimal partition problems, evolution flows, Cheeger-type problems, are also considered.

Keywords: shape optimization, capacity, optimization problems for eigenvalues, integral functionals