Spectral Optimization Problems

Details Spectral Optimization Problems Spectral Optimization Problems

2010-12-15

arxiv.org/abs/1012.3299v1

Mathematics

Optimization and Control

42 pages with 8 figures

Scientific paper

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.

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