5 papers
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 …
A Weierstrass extremal field theory for the fractional Laplacian
Xavier Cabre, Iñigo U. Erneta, Juan-Carlos Felipe-Navarro
In this paper we extend, for the first time, part of the Weierstrass extremal field theory in the Calculus of Variations to a nonlocal framework. Our model case is the energy funct…
Well-posedness for boundary value problems for coagulation-fragmentation equations
Iñigo U. Erneta
We investigate a coagulation-fragmentation equation with boundary data, establishing the well-posedness of the initial value problem when the coagulation kernels are bounded at zer…