Li, Congming; Liu, Chenkai; Wu, Zhigang; Xu, Hao Non-negative solutions to fractional Laplace equations with isolated singularity. (English) Zbl 1447.35083 Adv. Math. 373, Article ID 107329, 38 p. (2020). Summary: 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 \(L_{\text{loc}}^1\)-integrability. Furthermore, several basic lemmas are introduced to unify the treatments of Laplacian and fractional Laplacian. Cited in 7 Documents MSC: 35B50 Maximum principles in context of PDEs 35B09 Positive solutions to PDEs 35R11 Fractional partial differential equations 35B65 Smoothness and regularity of solutions to PDEs 35S05 Pseudodifferential operators as generalizations of partial differential operators Keywords:fractional Laplacian; singular solution; Bôcher theorem PDFBibTeX XMLCite \textit{C. Li} et al., Adv. Math. 373, Article ID 107329, 38 p. (2020; Zbl 1447.35083) Full Text: DOI References: [1] Axler, S.; Bourdon, P.; Ramey, W., Bôcher’s theorem, Am. Math. Mon., 99, 51-55 (1992) · Zbl 0758.31002 [2] Berestycki, H.; Nirenberg, L., Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations, J. Geom. Phys., 5, 237-275 (1988) · Zbl 0698.35031 [3] Berestycki, H.; Nirenberg, L., On the method of moving planes and the sliding method, Bol. Soc. Bras. Mat.-Bull./Braz. Math. Soc., 22, 1-37 (1991) · Zbl 0784.35025 [4] Berestycki, H.; Nirenberg, L.; Varadhan, S. 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