Revista Matemática Complutense

, Volume 24, Issue 2, pp 277–322 | Cite as

Spectral optimization problems

Article

Abstract

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

Optimization problems for eigenvalues Shape optimization Capacity Integral functionals Sobolev spaces Optimality conditions Calculus of variations Relaxation 

Mathematics Subject Classification (2000)

49J45 49R05 35P15 47A75 35J25 

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© Revista Matemática Complutense 2011

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di PisaPisaItaly

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