Liouville theorem and isolated singularity of fractional Laplacian system with critical exponents

2018/05/12 by Yimei Li, Jiguang Bao, Li, Yimei +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1805.06006

openalex publication_date 2018/05/12 · openalex created_date 2018/06/01 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the fractional Laplacian system with critical exponents. We use the method of moving sphere to derive a Liouville Theorem, and then prove the solutions in Rⁿ\0 are radially symmetric and monotonically decreasing radially. Together with blow up analysis and the Pohozaev integral, we get the upper and lower bound of the local solutions in B₁\0. Our results is an extension of the classical work by Caffarelli et al [6, 7], Chen et al[16]

Related

• Critical system involving fractional Laplacian
• Finite many critical problems involving Fractional Laplacians in ℝ^N
• The Neumann problem for a class of semilinear fractional equations with critical exponent
• Liouville type results for the fractional truncated Laplacians in a half-space
• Liouville theorem for singular solutions to nonlocal equations