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arXiv · 1805.06006

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

Yimei Li·Jiguang Bao
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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 R^n\{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 B_1\{0}. Our results is an extension of the classical work by Caffarelli et al [6, 7], Chen et al[16]

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Yimei Li, Jiguang Bao. 2018-05-12. Liouville theorem and isolated singularity of fractional Laplacian system with critical exponents. https://arxiv.org/abs/1805.06006

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