Partial differential equations, free boundaries and applications

本项目旨在研究偏微分方程分析和自由边界理论中的基本问题，发展具有重要应用可能性的先进数学理论。期望的结果是建立非局部方程的规则和分类理论以及线性和非线性设置下的自由边界问题。该项目的好处在于数学研究的具体推进，有利于对物理和生物学复杂现象的更深入的理解。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.