椭圆和抛物方程解的水平集的微观凸性

The microscopic convexity of level sets of solutions for elliptic and parabolic equations

偏微分方程解的水平集是一个重要研究对象,与偏微分方程解的存在性、唯一性和正则性紧密相关.本文介绍椭圆和抛物方程解的水平集的微观凸性原理.

The level set of solutions for elliptic and parabolic equations is an important research subject, and it has a close relation with the existence, uniqueness and regularity of solutions. In this paper, we introduce the microscopic convexity principles of level sets of solutions for elliptic and parabolic equations.