Studies on nonlinear partial differential equations via potential analysis

本文从位势论的观点出发，研究了区域的几何性质、方程的非线性性和非线性偏微分方程解的性质之间的关系。在非光滑区域上，我们得到了关于边界增长估计，Harnack型不等式，非切向极限的存在性，半线性椭圆型方程的保持器连续解的可去集的特征，半线性热方程的可去性定理以及热核的精确整体估计等结果.

We have investigated, from the point of view of potential theory, some relationships among geometric properties of domains, nonlinearity of equations and properties of solutions of nonlinear partial differential equations. In nonsmooth domains, we obtained several results concerning a boundary growth estimate, a Harnack type inequality, the existence of nontangential limits, a characterization of removable sets for Holder continuous solutions of semilinear elliptic equations, a removability theorem for semilinear heat equations and a sharp global estimate of the heat kernel.