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.
