8 papers · 1 filter
Regularity theory for fully nonlinear oblique transmission problems
Iñigo U. Erneta
We develop a regularity theory for fully nonlinear oblique transmission problems. Our main result establishes the optimal regularity of viscosity solutions for flat interfaces. For…
Fully nonlinear oblique transmission problems: Well-posedness
Iñigo U. Erneta
We introduce elliptic transmission problems involving fully nonlinear equations in both the interior bulk equations and the interface transmission condition. In contrast to all pre…
Lipschitz regularity for Poisson equations involving measures supported on interfaces
Iñigo U. Erneta, María Soria-Carro
We prove optimal Lipschitz regularity of solutions to Poisson's equation with measure data supported on a interface and with …
Null-Lagrangians and calibrations for general nonlocal functionals and an application to the viscosity theory
Xavier Cabre, Iñigo U. Erneta, Juan-Carlos Felipe-Navarro
In this article we build a null-Lagrangian and a calibration for general nonlocal elliptic functionals in the presence of a field of extremals. Thus, our construction assumes the e…
Energy estimate up to the boundary for stable solutions to semilinear elliptic problems
Iñigo U. Erneta
We obtain a universal energy estimate up to the boundary for stable solutions of semilinear equations with variable coefficients. Namely, we consider solutions to , w…
Boundary Hölder continuity of stable solutions to semilinear elliptic problems in domains
Iñigo U. Erneta
This article establishes the boundary Hölder continuity of stable solutions to semilinear elliptic problems in the optimal range of dimensions , for domains. We…