High-order estimates for fully nonlinear equations under weak concavity assumptions

2023/05/26 by Alessandro Goffi, Goffi, Alessandro · 4 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2305.17121

openalex publication_date 2023/05/26 · openalex created_date 2023/05/30 · openalex updated_date 2026/07/28

Abstract

This paper studies a priori and regularity estimates of Evans-Krylov type in Hölder spaces for fully nonlinear uniformly elliptic and parabolic equations of second order when the operator fails to be concave or convex in the space of symmetric matrices. In particular, it is assumed that either the level sets are convex or the operator is concave, convex or close to a linear function near infinity. As a byproduct, these results imply polynomial Liouville theorems for entire solutions of elliptic equations and for ancient solutions to parabolic problems.

Cited by

• Note on Regularity theory for Nonlinear elliptic equations
• On the smoothness of solutions of fully nonlinear second order equations in the plane
• Liouville theorems for fully nonlinear elliptic equations on half spaces
• A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications

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