Regularity and classification of solutions to static Hartree equations involving fractional Laplacians
RIS ID
132284
Abstract
In this paper, we are concerned with the fractional order equations (1) with Hartree type H α2 -critical nonlinearity and its equivalent integral equations (3). We first prove a regularity result which indicates that weak solutions are smooth (Theorem 1.2). Then, by applying the method of moving planes in integral forms, we prove that positive solutions u to (1) and (3) are radially symmetric about some point x0 ∈ Rd and derive the explicit forms for u (Theorem 1.3 and Corollary 1). As a consequence, we also derive the best constants and extremal functions in the corresponding Hardy-Littlewood-Sobolev inequalities (Corollary 2).
Publication Details
Dai, W., Huang, J., Qin, Y., Wang, B. & Fang, Y. (2019). Regularity and classification of solutions to static Hartree equations involving fractional Laplacians. Discrete and Continuous Dynamical Systems Series A, 39 (3), 1389-1403.