Abstract

We consider convex solutions of nonlinear elliptic equations which satisfy the structure condition of Bian and Guan. We prove a weak Harnack inequality for the eigenvalues of the Hessian of these solutions. This can be viewed as a quantitative version of the constant rank theorem.

中文翻译：

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特征值和常秩定理的弱 Harnack 不等式

摘要

我们考虑满足Bian和Guan结构条件的非线性椭圆方程的凸解。我们证明了这些解的 Hessian 特征值的弱 Harnack 不等式。这可以看作是常数秩定理的量化版本。