椭圆与抛物偏微分方程解的凸性

The Convexity of the Solution of Elliptic and Parabolic Partial Differential Equations

我们给出椭圆与抛物偏微分方程解或其水平集的凸性的一个文献综述.从三个经典例子开始,然后介绍凸性研究的常用方法,最后给出几个定量估计,其中注重与我个人研究有关的结果.

We give a survey on the convexity of the solutions or the level sets of the solution for elliptic and parabolic partial differential equations. We start three classical examples, then we introduce some usual methods in the study of convexity, at last we get some quantitative convexity estimates. We mainly concerns the results obtained by the author and his collaborator.