|Title||Regularity and classification of solutions to static Hartree equations involving Fractional Laplacians|
|Presenter||Yanqin Fang (University of Wollongong)|
|Session||Analysis and Partial Differential Equations|
We are concerned with the fractional order equations with Hartree type nonlinearity and its equivalent integral equations. We first prove a regularity result which indicates that weak solutions are smooth. Then, by applying the method of moving planes in integral forms, we prove that positive solutions of integral equations are radially symmetric about some point and derive the explicit forms of solutions. As a consequence, we also derive the best constants in the corresponding Hardy-Littlewood-Sobolev inequalities.
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