Mathematical Sciences: Viscosity Solutions of Nonlinear Partial Differential Equations

这个项目将考虑偏微分方程组的粘性解。研究具有可测系数的二阶椭圆型方程、极小曲面方程、p-拉普拉斯方程和有界域上某些柯西问题粘性解的唯一性。在初步结果的基础上，将发展各种最大值原理和正则性理论。虽然这个项目是针对偏微分方程的理论方面的，但其结果几乎立即在控制理论和金融等领域得到应用。

This project will consider viscosity solutions for partial differential equations. Uniqueness of viscosity solutions to second order elliptic equations with measurable coefficients, minimal surface equations, the p-Laplacian, and certain Cauchy problems in bounded domains will be studied. Based on preliminary results, various maximum principles and regularity theory will be developed. While this project is aimed at theoretical aspects of partial differential equations, the results have almost immediate applications in areas such as control theory and finance.