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math.AP2017
The closure of planar diffeomorphisms in Sobolev spaces
Guido De Philippis, Aldo Pratelli
We characterize the (sequentially) weak and strong closure of planar diffeomorphisms in the Sobolev topology and we show that they always coincide. We also provide some sufficient…
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 whose first eigenvalue is close to the one of the ball with the sa…