Dirichlet problems for fully nonlinear equations with \lq subquadratic \lq Hamiltonians

TL;DR

This paper establishes existence, uniqueness, and Lipschitz regularity of viscosity solutions for a class of fully nonlinear Dirichlet problems with singular or degenerate operators and subquadratic Hamiltonians.

Contribution

It introduces new results on the well-posedness and regularity of solutions for nonlinear PDEs with singular or degenerate structures and subquadratic growth conditions.

Findings

Existence of viscosity solutions for the class of equations.

Uniqueness of solutions under specified conditions.

Solutions are Lipschitz continuous.

Abstract

For a class of fully nonlinear equations having second order operators which may be singular or degenerate when the gradient of the solutions vanishes, and having first order terms with power growth, we prove the existence and uniqueness of suitably defined viscosity solution of Dirichlet problem and we further show that it is a Lipschitz continuous function.