9 citations · 37 across the 12 of their papers we have counts for
14 papers
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…
Elliptic regularization of some semilinear parabolic free boundary problems
Alessandro Audrito, Tomás Sanz-Perela
We prove existence of strong solutions to a family of some semilinear parabolic free boundary problems by means of elliptic regularization. Existence of solutions is obtained in tw…
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 condition…
A universal Hölder estimate up to dimension 4 for stable solutions to half-Laplacian semilinear equations
Xavier Cabre, Tomás Sanz-Perela
We study stable solutions to the equation , posed in a bounded domain of . For nonnegative convex nonlinearities, we prove that stable solutions…
Eigenvalue curves for generalized MIT bag models
Naiara Arrizabalaga, Albert Mas, Tomás Sanz-Perela +1
We study spectral properties of Dirac operators on bounded domains with boundary conditions of electrostatic and Lorentz scalar type and which depend on a p…
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…
Semilinear integro-differential equations, I: odd solutions with respect to the Simons cone
Juan-Carlos Felipe-Navarro, Tomás Sanz-Perela
This is the first of two papers concerning saddle-shaped solutions to the semilinear equation in , where is a linear elliptic integro-differen…
Uniqueness and stability of the saddle-shaped solution to the fractional Allen-Cahn equation
Juan-Carlos Felipe-Navarro, Tomás Sanz-Perela
In this paper we prove the uniqueness of the saddle-shaped solution to the semilinear nonlocal elliptic equation in , where and is…
Regularity of radial stable solutions to semilinear elliptic equations for the fractional Laplacian
Tomás Sanz-Perela
We study the regularity of stable solutions to the problem $$ \left\{ \begin{array}{rcll} (-Δ)^s u &=& f(u) & \text{in} \quad B_1\,, u &\equiv&0 & \text{in} \quad \mathbb R^n\setmi…
The wave equation for stiff strings and piano tuning
Xavier Gràcia, Tomás Sanz-Perela
We study the wave equation for a string with stiffness. We solve the equation and provide a uniqueness theorem with suitable boundary conditions. For a pinned string we compute the…