On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results

Abstract

We consider a nonlocal equation set in an unbounded domain with the epigraph property. We prove symmetry, monotonicity and rigidity results. In particular, we deal with halfspaces, coercive epigraphs and epigraphs that are flat at infinity.

Final version, accepted for publication on Mathematische Annalen

References in corpus (4)

• On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results
• Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
• On the fractional Lane-Emden equation
• Boundary regularity estimates for nonlocal elliptic equations in $C^1$ and $C^{1,\alpha }$ domains

Cited by in corpus (7)

• On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results
• An elliptic regularity theorem for fractional partial differential operators
• Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
• Maximum principles and the method of moving planes for the uniformly elliptic nonlocal Bellman operator and applications
• Maximum principles and monotonicity of solutions for fractional p-equations in unbounded domains
• Semilinear integro-differential equations, II: one-dimensional and saddle-shaped solutions to the Allen-Cahn equation
• Neumann conditions for the higher order $s$-fractional Laplacian $(-\Delta {)}^{s}u$ with $s>1$