Work

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

Year: 2024

Type: article

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.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2024.110800

Author: Alessandro Goffi

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,670

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", King Abdullah University of Science and Technology, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni

Awards: G1956684618, G2528524749, G3455614985, G5245466801