SYMMETRY OF POSITIVE SOLUTIONS FOR EQUATIONS INVOLVING HIGHER ORDER FRACTIONAL LAPLACIAN

摘要

In this paper, we consider problems associated with the higher order fractional Laplacian. Through the method of moving planes, we derive rotational symmetry of positive solutions and show their dependence on the x(n) variable only. We also establish the equivalence between a semilinear higher order fractional Laplacian equation and its corresponding integral equation, so as to further deduce a Liouville type theorem and obtain a priori estimates for positive solutions.