77 citations · 318 across the 51 of their papers we have counts for
6 papers · 2 filters
Regularity theory for general stable operators
Xavier Ros-Oton, Joaquim Serra
We establish sharp regularity estimates for solutions to in , being the generator of any stable and symmetric Lévy process. Such nonlocal operators…
Boundary regularity for the fractional heat equation
Xavier Fernández-Real, Xavier Ros-Oton
We study the regularity up to the boundary of solutions to fractional heat equation in bounded domains. More precisely, we consider solutions to $\partial_t u + (-Δ)^s u=…
Nonlocal problems with Neumann boundary conditions
Serena Dipierro, Xavier Ros-Oton, Enrico Valdinoci
We introduce a new Neumann problem for the fractional Laplacian arising from a simple probabilistic consideration, and we discuss the basic properties of this model. We can conside…
Local integration by parts and Pohozaev identities for higher order fractional Laplacians
Xavier Ros-Oton, Joaquim Serra
We establish an integration by parts formula in bounded domains for the higher order fractional Laplacian with . We also obtain the Pohozaev identity for this operato…
Boundary regularity for fully nonlinear integro-differential equations
Xavier Ros-Oton, Joaquim Serra
We study fine boundary regularity properties of solutions to fully nonlinear elliptic integro-differential equations of order , with . We consider the class of nonlo…
Regularity for the fractional Gelfand problem up to dimension 7
Xavier Ros-Oton
We study the problem in a bounded domain , where is a positive parameter. More precisely, we study the regularity of the extremal solution t…