5 papers
A fractional De Giorgi isoperimetric type inequality
Matteo Cozzi, Tomás Sanz-Perela
We establish an isoperimetric type inequality for the level sets of functions in fractional Sobolev spaces. This answers a question posed by the first author in a previous paper. T…
A connection between quantum dot Dirac operators and -Robin Laplacians in the context of shape optimization problems
Joaquim Duran, Albert Mas, Tomás Sanz-Perela
This work addresses Faber-Krahn-type inequalities for quantum dot Dirac operators with nonnegative mass on bounded domains in . We show that this family of inequaliti…
On the existence of solutions to some singular parabolic free boundary problems
Alessandro Audrito, Tomás Sanz-Perela
We construct nonnegative weak solutions to the singular parabolic free boundary problem \[ \partial_t u - Îu = - \frac{\mathrm{d}}{\mathrm{d} u} u_+^γ, \] where , $u…
Stable cones in the Alt-Phillips free boundary problem
Aram Karakhanyan, Tomás Sanz-Perela
In this paper we prove a classification result for axially symmetric one phase minimizers of the Alt-Phillips free boundary problem in dimensions 3, 4, and 5. To accomplish this, w…
Stable solutions to fractional semilinear equations: uniqueness, classification, and approximation results
Tomás Sanz-Perela
We study stable solutions to fractional semilinear equations in , for convex nonlinearities , and under the Dirichlet exterior conditi…