椭圆偏微分方程解的凸性研究综述

Survey on Convexity of Solutions of Elliptic Partial Differential Equations

综述介绍了椭圆偏微分方程解的凸性研究的方法、研究现状.用凹性极大值原理来处理解的凸性问题是一种宏观的方法,常秩定理则是从微观的角度来处理解的凸性问题,由于常秩定理是强极值原理,因而能够得到解的严格凸性.

Main methods and current research status of convexity of solutions of elliptic partial differential equations are outlined.From the point of macroscopic view,the method is using concavity maximum principle.From the point of microcosmic view,the method is using constant rank theorem.Because constant rank theorem is strong maximum principle,strictly convexity of solutions can be obtained.