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Main Author: Fan, Zhenyu
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2509.01138
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author Fan, Zhenyu
author_facet Fan, Zhenyu
contents In this note, we generalize Savin's small perturbation theorem to nonhomogeneous fully nonlinear equations $F(D^2u, Du, u,x)=f$ provided the coefficients and the right-hand side terms are Hölder small perturbations. As an application, we establish a partial regularity result for the sigma-$k$ Hessian equation $σ_{k}(D^2u)=f$.
format Preprint
id arxiv_https___arxiv_org_abs_2509_01138
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications
Fan, Zhenyu
Analysis of PDEs
In this note, we generalize Savin's small perturbation theorem to nonhomogeneous fully nonlinear equations $F(D^2u, Du, u,x)=f$ provided the coefficients and the right-hand side terms are Hölder small perturbations. As an application, we establish a partial regularity result for the sigma-$k$ Hessian equation $σ_{k}(D^2u)=f$.
title A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications
topic Analysis of PDEs
url https://arxiv.org/abs/2509.01138