Mathematics > Analysis of PDEs
[Submitted on 1 Sep 2025
]
Title: A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications
Title: 完全非线性椭圆方程的Savin小扰动定理的推广及其应用
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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