Liouville theorems involving the fractional Laplacian on a half space
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 , 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
Please refer to publisher version or contact your library.