7 papers · 1 filter
A Payne-Weinberger inequality for quantum dot Dirac operators
Joaquim Duran, Albert Mas, Tomás Sanz-Perela
In this work we prove a Payne-Weinberger type inequality for quantum dot Dirac operators defined on bounded and simply connected planar domains. This is a sharp upper bound for the…
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…
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 \[ \partial_t u - Δu = - \frac{\mathrm{d}}{\mathrm{d} u} u_+^γ, \] where , $u_+…
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…
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…
Semilinear integro-differential equations, II: one-dimensional and saddle-shaped solutions to the Allen-Cahn equation
Juan-Carlos Felipe-Navarro, Tomás Sanz-Perela
This paper addresses saddle-shaped solutions to the semilinear equation in , where is a linear elliptic integro-differential operator with a r…