通用积分特性及其在反向塞林问题中的应用

Rolando Magnanini, Riccardo Molinarolo, Giorgio Poggesi
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引用次数: 0

摘要

我们证明了一个新的一般微分特性和相关积分特性,它包含一对具有常数源项的泊松方程解。这概括了第一作者和第三作者先前证明并用于获得塞林超定边界值问题球面对称性定量估计的公式。作为应用,我们证明了反向 Serrin 问题的定量对称性结果,这也是我们在本文中首次提出的。顺带一提,我们还获得了上述泊松方程在恒定诺伊曼条件下的解的刚性结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A General Integral Identity with Applications to a Reverse Serrin Problem

We prove a new general differential identity and an associated integral identity, which entails a pair of solutions of the Poisson equation with constant source term. This generalizes a formula that the first and third authors previously proved and used to obtain quantitative estimates of spherical symmetry for the Serrin overdetermined boundary value problem. As an application, we prove a quantitative symmetry result for the reverse Serrin problem, which we introduce for the first time in this paper. In passing, we obtain a rigidity result for solutions of the aforementioned Poisson equation subject to a constant Neumann condition.

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