走向现代数学学术报告 - 鲁志豪博士生（No. 610）

题目：Introduction to Bernstein method and its applications

报告人：鲁志豪（中国科学技术大学）

时间：2023年5月12日（星期五）19:00

地点：工西417

摘要：In 1906 and 1910, S. Bernstein provide a method to get gradient estimate for harmonic functions on Euclidean spaces. The basic method gives a completely new technique to get prior estimates for second order elliptic and parabolic equations. The core of this method is the construction of auxiliary functions associated with solutions. In 1970s and 1980s, the work of Yau and Li-Yau found the famous logarithmic gradient estimate for positive solutions of Laplacian equation and heat equation on the Riemannian manifolds with Ricci bounded below by this method. In this talk, we use this method to get logarithmic gradient estimate and universal boundedness estimates for semilinear elliptic equations on same setting under sub-critical index condition for all dimensions.

报告人简介：鲁志豪，中国科学技术大学数学学科学院在读博士生，目前主要从事有曲率下界的黎曼流形以及有曲率维数条件的度量测度空间上的椭圆和抛物方程的正解的定量研究。