Partial differential equations, free boundaries and applications

这个项目的目的是研究偏微分方程和自由边界理论分析中的基本问题，发展具有重要应用可能性的高级数学理论。预期的结果是为非局部方程和线性和非线性环境中的自由边界问题建立一个正则性和分类理论。该项目的好处在于数学研究的具体进展，有利于更深入地理解物理和生物学中的复杂现象。其中一些问题也为工业应用提供了有用的结果。

This project aims to investigate fundamental problems in the analysis of partial differential equations and free boundary theory, to develop advanced mathematical theories with the possibility of important applications. The expected outcome is the establishment of a regularity and classification theory for nonlocal equations and for free boundary problems in linear and nonlinear settings. The benefit of the project lies in a concrete advancement of the mathematical research with advantages for a deeper understanding of complex phenomena in physics and biology. Some of the problems also provide results useful for industrial applications.