The seminar is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.
In this talk, I would like to introduce the radial symmetry and monotonicity properties of positive solutions to fractional elliptic equations. Symmetry result for equations involving the fractional laplacian was initiated with the work by Li and Chen-Li-Ou, with the method of moving planes in integral form, where need the condition of the nonlinearity is increasing. While we make use of ABP estimate and the Maximum principle for small domain to obtain the symmetric property by the method of moving planes without increasing monotonicity for the nonlinearity.
Dr. Ying Wang holds her Ph.D. from Universidad de Chile, Chile in June 2015. Now she is a visiting scholar of Center for Partial Differential Equations in ECNU. Dr. Wang’s research interests are elliptic equations involving nonlocal operators. Her work has appeared in the Communications in Contemporary Mathematics, Nonlinear Analysis and Discrete and Continuous Dynamical Systems - Series A.