Title：Pointwise gradient estimates via two-point functions for elliptic equations on manifolds

Speaker：熊昌伟 （澳洲国立大学）

Time：2019年3月28日        下午  16:00-17:00

Room：东区管理科研楼  0029cc金沙贵宾会1318室

Abstract：Pointwise gradient estimates for bounded solutions of elliptic equations on Euclidean space have attracted much attention since the study by L. Modica in 1985. Most of them are known to be proved by the P-function method, a method which seems to work only for equations of variational structure. In this talk we will present how to employ the two-point functions method to derive these pointwise gradient estimates. Moreover, it turns out that the method by two-point functions can apply well to a much wider class of elliptic equations on Euclidean space, and also to the problems on Riemannian manifolds and Finsler manifolds with suitable lower bounds on (weighted) Ricci curvature. This is a joint work with Ben Andrews.