Mathematical Sciences: Viscosity Solutions of Nonlinear Partial Differential Equations

该项目将考虑部分粘度解决方案 微分方程 粘度溶液的均一性 二阶可测系数椭圆方程 最小曲面方程，p-Laplacian，和某些Cauchy 将研究有界域中的问题。 基于 初步结果，各种极大值原理和规律 理论将得到发展。 虽然这个项目的目的是在理论方面， 偏微分方程，结果几乎立即 在控制理论和金融等领域的应用。

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.