A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications

Zhenyu Fan

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arXiv · 2509.01138

A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications

Zhenyu Fan

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Abstract

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 H\"older small perturbations. As an application, we establish a partial regularity result for the sigma-$k$ Hessian equation $\sigma_{k}(D^2u)=f$.

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Zhenyu Fan. 2025-09-01. A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications. https://arxiv.org/abs/2509.01138

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