A. Pratelli

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20122020

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math.OC2017

Some estimates for the higher eigenvalues of sets close to the ball

Dario Mazzoleni, Aldo Pratelli

In this paper we investigate the behavior of the eigenvalues of the Dirichlet Laplacian on sets in $R^{N}$ whose first eigenvalue is close to the one of the ball with the sa…

math.OC2015

Regularity of isoperimetric sets in $R^{2}$ with density

Eleonora Cinti, Aldo Pratelli

We consider the isoperimetric problem in $R^{n}$ with density for the planar case $n = 2$ . We show that, if the density is $C^{0, α}$ , then the boundary of any isoperimetr…

Some estimates for the higher eigenvalues of sets close to the ball

Regularity of isoperimetric sets in R2 with density

Regularity of isoperimetric sets in $R^{2}$ with density