Xavier Ros-Oton

activity

20112026

most citedBoundary regularity for fully nonlinear integro-differential equations

77 citations · 318 across the 51 of their papers we have counts for

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Showing 2014Show all

6 papers · 1 filter

math.AP2014

Regularity theory for general stable operators

Xavier Ros-Oton, Joaquim Serra

We establish sharp regularity estimates for solutions to $Lu = f$ in $Ω \subset R^{n}$ , being $L$ the generator of any stable and symmetric Lévy process. Such nonlocal operators…

math.AP2014

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 $C^{1, 1}$ domains. More precisely, we consider solutions to $\partial_t u + (-Δ)^s u=…

math.AP2014

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…

math.AP2014★ 4 cited

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 $(- Δ)^{s}$ with $s > 1$ . We also obtain the Pohozaev identity for this operato…

math.AP2014★ 77 cited

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 $2 s$ , with $s \in (0, 1)$ . We consider the class of nonlo…

math.AP2014

Regularity for the fractional Gelfand problem up to dimension 7

Xavier Ros-Oton

We study the problem $(- Δ)^{s} u = λ e^{u}$ in a bounded domain $Ω \subset R^{n}$ , where $λ$ is a positive parameter. More precisely, we study the regularity of the extremal solution t…