Title

Liouville theorems involving the fractional Laplacian on a half space

RIS ID

112119

Publication Details

Chen, W., Fang, Y. & Yang, R. (2015). Liouville theorems involving the fractional Laplacian on a half space. Advances in Mathematics, 274 167-198.

Abstract

Let R+ n be the upper half Euclidean space and let α 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 [8], we employ a new and direct approach by studying an equivalent integral equation. Applying the method of moving planes in integral forms, we prove the non-existence of positive solutions in the critical and subcritical cases under no restrictions on the growth of the solutions

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Link to publisher version (DOI)

http://dx.doi.org/10.1016/j.aim.2014.12.013