Elliptic gradient constraint problem

Abstract

ABSTRACTWe study the existence and regularity of gradient constraint problem. It arises in elastoplasticity and finance. First, we consider linear double obstacle problem which comes from viscosity solution to Hamilton–Jacobi equation and find the solution has C1,α regularity by estimating Campanato-type integral oscillation. Then, by perturbation method and fixed point theorem in C1,α space, we prove the existence of C1,α solution.