Non-negative solutions to fractional Laplace equations with isolated singularity

Non-negative solutions to fractional Laplace equations with isolated singularity

In this paper, we study singular solutions of linear problems with fractional Laplacian. First, we establish Bôcher type theorems on a punctured ball via distributional approach. Then, we develop a few interesting maximum principles on a punctured ball. Our distributional approach only requires the...

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2020-10, Vol.373, p.107329, Article 107329
Hauptverfasser: Li, Congming, Liu, Chenkai, Wu, Zhigang, Xu, Hao
Format: Artikel
Sprache:eng
Schlagworte:
Bôcher theorem
Fractional Laplacian
Mathematics
Maximum principle
Physical Sciences
Science & Technology
Singular solution
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Zusammenfassung:In this paper, we study singular solutions of linear problems with fractional Laplacian. First, we establish Bôcher type theorems on a punctured ball via distributional approach. Then, we develop a few interesting maximum principles on a punctured ball. Our distributional approach only requires the basic Lloc1-integrability. Furthermore, several basic lemmas are introduced to unify the treatments of Laplacian and fractional Laplacian.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2020.107329