9 papers · 1 filter
Boundary regularity of harmonic functions in slit domains
Joan Domingo-Pasarin, Pablo Hidalgo-Palencia, Alejandro Martínez +1
We establish precise upper and lower estimates for harmonic functions vanishing on the slit of a slit domain, with no assumption that the slit lies in a hyperplane. The class…
Minimizers for Coulomb gases constrained to a halfspace
Rupert L. Frank, Paata Ivanisvili, Clara Torres-Latorre
We consider a family of optimization problems, based on a mean-field description of particles interacting through Coulomb forces in a quadratic trap. In addition, the particles are…
Boundary estimates for parabolic non-divergence equations in domains
Pêdra D. S. Andrade, Clara Torres-Latorre
We obtain boundary nondegeneracy and regularity estimates for solutions to non-divergence form parabolic equations in parabolic domains, providing explicit moduli of continui…
Existence and nonexistence of infinitely many solutions to elliptic problems with oscillating nonlinearities
Antonio J. Martínez Aparicio, Clara Torres-Latorre
We study sharp conditions for the existence and nonexistence of infinitely many nonnegative solutions to the problem in a bounded domain with Dirichlet boundary co…
The Pohozaev identity for the Spectral Fractional Laplacian
Itahisa Barrios-Cubas, Matteo Bonforte, María del Mar González +1
In this paper, we prove a Pohozaev identity for the Spectral Fractional Laplacian (SFL). This identity allows us to establish non-existence results for the semilinear Dirichlet pro…
Extinction rates for nonradial solutions to the Stefan problem
Gabriele Fioravanti, Xavier Ros-Oton, Clara Torres-Latorre
We consider the one-phase Stefan problem describing the evolution of melting ice. On the one hand, we focus on understanding the evolution of the free boundary near isolated singul…