Non-negative solutions to fractional Laplace equations with isolated singularity

被引：13

作者：

Li, Congming ^{[1
,3
]}

Liu, Chenkai ^{[1
]}

Wu, Zhigang ^{[2
]}

Xu, Hao ^{[3
]}

机构：

[1] Shanghai Jiao Tong Univ, Sch Math Sci, MOE LSC, Shanghai, Peoples R China

[2] Donghua Univ, Dept Math, Shanghai, Peoples R China

[3] Univ Colorado Boulder, Dept Appl Math, Boulder, CO USA

来源：

ADVANCES IN MATHEMATICS | 2020年 / 373卷

关键词：

Fractional Laplacian; Singular solution; Bocher theorem; Maximum principle; SEMILINEAR ELLIPTIC-EQUATIONS; MAXIMUM-PRINCIPLES; ASYMPTOTIC SYMMETRY; POSITIVE SOLUTIONS; KLEINIAN-GROUPS; LOCAL BEHAVIOR; HARMONIC MAPS; REGULARITY; CLASSIFICATION; CURVATURE;

D O I：

10.1016/j.aim.2020.107329

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study singular solutions of linear problems with fractional Laplacian. First, we establish Bocher 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-loc(1)-integrability. Furthermore, several basic lemmas are introduced to unify the treatments of Laplacian and fractional Laplacian. (C) 2020 Published by Elsevier Inc.

引用

页数：38

共 40 条

[1] [Anonymous], 1981, Mathematical analysis and applications, Part A, Adv. Math. Suppl. Stud.
[2] BOCHER THEOREM
AXLER, S
BOURDON, P
RAMEY, W
[J]. AMERICAN MATHEMATICAL MONTHLY, 1992, 99 (01) : 51 - 55
[3] THE PRINCIPAL EIGENVALUE AND MAXIMUM PRINCIPLE FOR 2ND-ORDER ELLIPTIC-OPERATORS IN GENERAL DOMAINS
BERESTYCKI, H
NIRENBERG, L
VARADHAN, SRS
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1994, 47 (01) : 47 - 92
[4] Berestycki H., 1988, Journal of Geometry and Physics, V5, P237, DOI DOI 10.1016/0393-0440(88)90006-X
[5] Berestycki H., 1991, Bol. Soc. Bras. Mat., V22, P1, DOI DOI 10.1007/BF01244896
[6] Bocher M., 1903, Bull. Amer. Math. Soc, V9, P455, DOI DOI 10.1090/S0002-9904-1903-01017-9
[7] SOME OBSERVATIONS ON THE GREEN FUNCTION FOR THE BALL IN THE FRACTIONAL LAPLACE FRAMEWORK
Bucur, Claudia
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2016, 15 (02) : 657 - 699
[8] Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates
Cabre, Xavier
Sire, Yannick
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2014, 31 (01): : 23 - 53
[9] ASYMPTOTIC SYMMETRY AND LOCAL BEHAVIOR OF SEMILINEAR ELLIPTIC-EQUATIONS WITH CRITICAL SOBOLEV GROWTH
CAFFARELLI, LA
GIDAS, B
SPRUCK, J
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1989, 42 (03) : 271 - 297
[10] Regularity Theory for Fully Nonlinear Integro-Differential Equations
Caffarelli, Luis
Silvestre, Luis
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2009, 62 (05) : 597 - 638

← 1 2 3 4 →