发表机构
University of Tennessee（田纳西大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对仅在解梯度位于闭球和闭纯一维不可求集外时成立的完全非线性一致椭圆方程，证明了与例外集无关的粘性解的哈纳克不等式和赫尔德正则性估计，还通过例子和反例说明纯一维不可求性的作用，且内容自包含。
AI 中文摘要
我们研究完全非线性一致椭圆方程，这些方程仅在解的梯度位于闭球和闭纯一维不可求集（该集可以是无界的）之外时才被施加。我们证明了粘性解的哈纳克不等式和赫尔德正则性估计，其常数与例外集无关。证明利用了尖点接触集的几何和障碍论证来排除例外梯度。我们还提供了例子和反例，以说明纯一维不可求性的作用。材料和证明被详细呈现，以确保论文完全自包含且能被广泛读者理解。
英文摘要
We study fully nonlinear uniformly elliptic equations that are imposed only when the gradients of solutions lie outside a closed ball and a closed purely one-unrectifiable set that can be unbounded. We prove Harnack inequalities and Hölder regularity estimates for viscosity solutions, with constants independent of the exceptional set. The proofs use the geometry of the contact sets in the cusp and barrier arguments to exclude exceptional gradients. We also provide examples and counterexamples showing the role of pure one-unrectifiability. Materials and proofs are presented in detail to ensure the paper is fully self-contained and accessible to a broad audience.
Comments30 pages, comments are welcome
