Interior Hölder and Calderón-Zygmund estimates for fully nonlinear equations with natural gradient growth

2023/12/06 by Goffi, Alessandro
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.03522

Abstract

We establish local Hölder estimates for viscosity solutions of fully nonlinear second order equations with quadratic growth in the gradient and unbounded right-hand side in L^q spaces, for an integrability threshold q guaranteeing the validity of the maximum principle. This is done through a nonlinear Harnack inequality for nonhomogeneous equations driven by a uniformly elliptic Isaacs operator and perturbed by a Hamiltonian term with natural growth in the gradient. As a byproduct, we derive a new Liouville property for entire L^p viscosity solutions of fully nonlinear equations as well as a nonlinear Calderón-Zygmund estimate for strong solutions of such equations.

Related

• Holder regularity for fully nonlinear nonlocal equations
• Uniform bounds via regularity estimates for elliptic PDE with critical growth in the gradient
• Regularity estimates for fully nonlinear elliptic PDEs with general\n Hamiltonian terms and unbounded ingredients
• Global Calderón-Zygmund estimates for asymptotically convex fully nonlinear Grad-Mercier type equations
• Hôlder continuity of solutions of second-order non-linear elliptic integro-differential equations