Semilinear equations involving the fractional Laplacian on domains

Abstract

Applying the method of moving planes in integral forms, we establish radial symmetry for positive solutions to a class of semilinear equations involving the fractional Laplacian in the unit ball and obtain Liouville type theorems concerning the non-existence of positive solutions in the half space. The regularity of solutions are also investigated.

References in corpus (1)

• Fractional dynamics of systems with long-range interaction

Cited by in corpus (4)

• Existence, Non-existence, Uniqueness of solutions for semilinear elliptic equations involving measures concentrated on boundary
• Negative Power Nonlinear Integral Equations on Bounded Domains
• A semilinear equation involving the fractional Laplacian in ${\mathbb{R}}^n$
• Certain fractional Laplacian equations that do not have smooth solutions