发表机构
School of Mathematics and Physics, University of Science and Technology Beijing（北京科技大学数学与物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对半空间中带非局部Neumann边界条件的分数阶拉普拉斯方程（含方程组），通过建立衰减原理和窄区域原理，结合移动平面法，首次证明了衰减解的对称性与单调性。
AI 中文摘要
本文研究了半空间中的分数阶拉普拉斯方程，特别关注具有非局部Neumann边界条件的情形。我们同时考虑了单个方程和方程组，并建立了两个关键原理：无穷远处的衰减原理和窄区域原理。这些基础性结果，结合移动平面的直接方法，使我们能够推导出衰减解的对称性和单调性性质。据我们所知，这是关于具有非局部Neumann条件的分数阶拉普拉斯方程解的对称性的首批结果。
英文摘要
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.
Comments20 pages
