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arXiv · 2312.03522

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

Alessandro Goffi
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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.

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Alessandro Goffi. 2024-10-14. Interior Hölder and Calderón-Zygmund estimates for fully nonlinear equations with natural gradient growth. https://arxiv.org/abs/2312.03522

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