PDE Seminar Abstracts

Regularity and classification of solutions to static Hartree equations involving Fractional Laplacians

Yanqin Fang
University of Wollongong
Mon 4th Sep 2017, 2-3pm, Carslaw Room 829 (AGR)

Abstract

We are concerned with the fractional order equations with Hartree type nonlinearity and its equivalent integral equations. We rst prove a regularity result which indicates that weak solutions are smooth. Then, by applying the method of moving planes in integral form, we prove that positive solutions of integral equations are radially symmetric about some point and derive the explicit form of solutions. As a consequence, we also derive the best constants in the corresponding Hardy-Littlewood-Sobolev inequalities.