报告题目：Symmetry Results for Semilinear Local and Nonlocal Elliptic PDEs
报告人：Mostafa Fazly 博士（University of Alberta, Canada）
时间：2014年 12月 5日（周五）上午10: 30--11: 30 
地点：综合楼三楼会议室
摘要：We start this talk with a celebrated conjecture of De Giorgi on bounded monotone solutions of the Allen-Cahn equation. De Giorgi's conjecture (1978) brings together three groups of mathematicians: one specializing in nonlinear partial differential equations, another in differential geometry, more specially on minimal surfaces and constant mean curvature surfaces, and in mathematical physics on phase transitions. The main focus of this talk is on ideas and methods developed regarding this conjecture from PDE perspectives. We then state counterparts of this conjecture to various local and nonlocal elliptic PDEs and provide the known results. The main challenges in this topic are mostly proving monotonicity formula, linear Liouville theorems and pointwise/Hamiltonian estimates.