Symmetry of solutions to nonlocal Neumann problems with the fractional Laplacian in half spaces
Year: 2026
Type: preprint
Abstract: This paper investigates the fractional Laplacian equation in half-spaces, focusing on cases with nonlocal Neumann boundary conditions. We consider both single equations and systems, and establish two key principles: the decay at infinity principle and the narrow region principle. These foundational results, combined with the direct method of moving planes, allow us to derive symmetry and monotonicity properties for decaying solutions. To the best of our knowledge, these are the first results concerning the symmetry of solutions to fractional Laplacian equations with nonlocal Neumann conditions.
Source: arXiv (Cornell University)
Authors: Liu, Baiyu, Tan, Wenli
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4098811570
OpenAlex ID: W7214793775