8 citations · 25 across the 8 of their papers we have counts for
8 papers
Uniform a priori estimates for slightly subcritical fractional problems
Juan-Carlos Felipe-Navarro, Rosa Pardo
We study the uniform a priori boundedness of positive weak solutions to the fractional semilinear Dirichlet problem in a bounded, convex, …
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…
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…
Uniqueness for linear integro-differential equations in the real line and applications
Juan-Carlos Felipe-Navarro
In this work we prove the uniqueness of solutions to the nonlocal linear equation in , where is an elliptic integro-differential operator, in the pr…
The Neumann problem for the fractional Laplacian: regularity up to the boundary
Alessandro Audrito, Juan-Carlos Felipe-Navarro, Xavier Ros-Oton
We study the regularity up to the boundary of solutions to the Neumann problem for the fractional Laplacian. We prove that if is a weak solution of in , $\mathc…
Semilinear integro-differential equations, II: one-dimensional and saddle-shaped solutions to the Allen-Cahn equation
Juan-Carlos Felipe-Navarro, Tomás Sanz-Perela
This paper addresses saddle-shaped solutions to the semilinear equation in , where is a linear elliptic integro-differential operator with a r…
Semilinear integro-differential equations, I: odd solutions with respect to the Simons cone
Juan-Carlos Felipe-Navarro, Tomás Sanz-Perela
This is the first of two papers concerning saddle-shaped solutions to the semilinear equation in , where is a linear elliptic integro-differen…
Uniqueness and stability of the saddle-shaped solution to the fractional Allen-Cahn equation
Juan-Carlos Felipe-Navarro, Tomás Sanz-Perela
In this paper we prove the uniqueness of the saddle-shaped solution to the semilinear nonlocal elliptic equation in , where and is…