一个应用于反向Serrin问题的通用积分恒等式
A general integral identity with applications to a reverse Serrin problem
AI总结：
该研究提出新的通用微分与积分恒等式，推广了此前Serrin问题相关公式，并首次引入反向Serrin问题，证明其定量对称性结果，还得到对应Poisson方程解的刚性结果。
摘要：
我们证明了一个新的通用微分恒等式及相关积分恒等式，该恒等式涉及一对带常数源项的Poisson方程的解。这推广了第一和第三作者此前证明并用于获得Serrin超定边值问题球对称性定量估计的一个公式。作为应用，我们证明了本文首次提出的反向Serrin问题的定量对称性结果。顺带地，我们得到了上述满足常数Neumann条件的Poisson方程解的一个刚性结果。
英文摘要：
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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