几类测度数据下非线性椭圆和抛物型方程解的Calderón-Zygmund正则性

近年来，源于等离子体物理学、流体力学、等多孔介质等实际问题的右端项为L^1函数或Radon测度的椭圆和抛物型方程解的正则性吸引了大量研究人员的兴趣。本项目拟综合运用扰动技术、内蕴几何方法和双参数技术等研究几类非线性方程的Calderón-Zygmund正则性，主要包括以下三部分：（1）针对右端项为L^1函数或Radon测度且满足p-增长条件的非线性椭圆方程，研究其解的Calderón-Zygmund型估计。（2）针对右端项为L^1函数或Radon测度且满足p-增长条件的非线性抛物方程，研究其解的Calderón-Zygmund型估计。（3）针对右端项为L^1函数或Radon测度且满足非标准增长条件的非线性椭圆和抛物方程，研究其解的非线性Calderón-Zygmund型估计。本项目的研究成果将在很大程度上拓展非线性偏微分方程的Calderón-Zygmund理论。

In recent years, a large number of researchers have been interested in the regularity of solutions to elliptic and parabolic equations with L^1 function or Radon measure, which arise naturally from practical problems such as plasma physics, fluid mechanics, porous media and so on. This project is devoted to studing the Calderón-Zygmund regularity of several kinds of nonlinear equations by using perturbation technique, intrinsic geometry method and two parameters technique, etc, which includes the following three parts: (1) The main purpose is to study the Calderón-Zygmund type estimates of solutions to nonlinear elliptic equations with L^1 function or Radon measure and satisfying p-growth condition; (2) For nonlinear parabolic equations with L^1 function or Radon measure and satisfying p-growth condition, the main purpose is to study the Calderón-Zygmund type estimates of their solutions; (3) We study the nonlinear Calderón-Zygmund type estimates of solutions to nonlinear elliptic and parabolic equations with L^1 function or Radon measure and satisfying nonstandard growth condition. The results of this project will greatly expand the Calderón-Zygmund theory of nonlinear partial differential equations.