6 papers
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…
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…
On the piecewise approximation of bi-Lipschitz curves
Aldo Pratelli, Emanuela Radici
In this paper we deal with the task of uniformly approximating an -biLipschitz curve by means of piecewise linear ones. This is rather simple if one is satisfied to have approxi…
Regularity of isoperimetric sets in with density
Eleonora Cinti, Aldo Pratelli
We consider the isoperimetric problem in with density for the planar case . We show that, if the density is , then the boundary of any isoperimetr…
Diffeomorphic Approximation of Planar Sobolev Homeomorphisms
Stanislav Hencl, Aldo Pratelli
Let be a domain and let be a homeomorphism (between and ). Then there exists a sequence of smooth diffeomorphisms $f…
The property, the boundedness of isoperimetric sets in with density, and some applications
Eleonora Cinti, Aldo Pratelli
We show that every isoperimetric set in R^N with density is bounded if the density is continuous and bounded by above and below. This improves the previously known boundedness resu…