Calculus of Variations and Geometric Measure Theory

Concentration-compactness principle and shape optimization problems

Bozhidar Velichkov (Università di Pisa)

created by magnani on 16 May 2011

25 may 2011


Dipartimento di Matematica - Sala Seminari - ore 17:00

ABSTRACT: We expose an existence result for a shape optimization problem in the Euclidean space. During this seminar we will show that, given an arbitrary open set A of unitary measure, there exists at least one quasi-open set which minimizes the rst eigenvalue of the Dirichlet laplacian among all quasi-open sets, containing A, with a xed positive Lebesgue measure (greater than one). The proof is based on a concentration-compactness principle for quasi-open sets which was introduced by Dorin Bocur as a natural extension of the classical result due to Lions. The result is joint with Giuseppe Buttazzo and Dorin Bucur.