526 citations
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Showing 2013 · math.APShow all
3 papers · 2 filters
math.AP2013★ 101 cited
Faber-Krahn inequalities in sharp quantitative form
Lorenzo Brasco, Guido De Philippis, Bozhidar Velichkov
The classical Faber-Krahn inequality asserts that balls (uniquely) minimize the first eigenvalue of the Dirichlet-Laplacian among sets with given volume. In this paper we prove a s…
math.AP2013★ 9 cited
Higher integrability for minimizers of the Mumford-Shah functional
Guido De Philippis, Alessio Figalli
We prove higher integrability for the gradient of local minimizers of the Mumford-Shah energy functional, providing a positive answer to a conjecture of De Giorgi.
math.AP2013★ 2 cited
Existence and regularity of minimizers for some spectral functionals with perimeter constraint
Guido De Philippis, Bozhidar Velichkov
In this paper we prove that the shape optimization problem has a solution for any and…