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期刊名称: Advances in Mathematics
Volume:274    Page:167-198
ISSN:0001-8708

Liouville theorems involving the fractional Laplacian on a half space期刊论文

作者: Chen Wenxiong Fang Yanqin Yang Ray
DOI:10.1016/j.aim.2014.12.013

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页码: 167-198
被引频次: 55
出版者: Elsevier Inc,ACADEMIC PRESS INC ELSEVIER SCIENCE,Elsevier B.V
期刊名称: Advances in Mathematics
ISSN: 0001-8708
语言: English
摘要: Let be the upper half Euclidean space and let be any real number between 0 and 2. Consider the following Dirichlet problem involving the fractional Laplacian: Instead of using the conventional extension method of Caffarelli and Silvestre , we employ a new and direct approach by studying an equivalent integral equation Applying the , we prove the non-existence of positive solutions in the critical and subcritical cases under no restrictions on the growth of the solutions.
相关主题: Liouville theorems, Method of moving planes in integral forms, Semi-linear elliptic equation, Dirichlet problem, Non-existence, Green's function, Integral equation, The fractional Laplacian, Half space, Monotonicity, Symmetry, The fractional laplacian, SYSTEM, INTEGRAL-EQUATION, MATHEMATICS, RADIAL SYMMETRY, HARMONIC DIRICHLET PROBLEMS, REGULARITY, WOLFF TYPE, Jewish schools,

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