带罗宾边界条件的 p 拉普拉斯泊松问题的刚性结果

IF 1.6 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Optimization Theory and Applications Pub Date : 2024-05-14 DOI:10.1007/s10957-024-02442-1

Alba Lia Masiello, Gloria Paoli

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引用次数: 0

摘要

让 \(\Omega \subset \mathbb {R}^n\) 是一个开放的、有界的和 Lipschitz 集。我们考虑与 Robin 边界条件相关的 p-Laplace 算子的泊松问题。在这种情况下，我们研究了 Talenti 型比较中的相等情况：我们证明只有当 \(\Omega \) 是一个球，并且泊松方程的解 u 和右边 f 都是径向递减时，相等才会实现。

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Rigidity Results for the p-Laplacian Poisson Problem with Robin Boundary Conditions

Let \(\Omega \subset \mathbb {R}^n\) be an open, bounded and Lipschitz set. We consider the Poisson problem for the p-Laplace operator associated to \(\Omega \) with Robin boundary conditions. In this setting, we study the equality case in the Talenti-type comparison: we prove that the equality is achieved only if \(\Omega \) is a ball and both the solution u and the right-hand side f of the Poisson equation are radial and decreasing.

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来源期刊

Journal of Optimization Theory and Applications 数学-应用数学

CiteScore

3.30

自引率

5.30%

发文量

149

审稿时长

9.9 months

期刊介绍： The Journal of Optimization Theory and Applications is devoted to the publication of carefully selected regular papers, invited papers, survey papers, technical notes, book notices, and forums that cover mathematical optimization techniques and their applications to science and engineering. Typical theoretical areas include linear, nonlinear, mathematical, and dynamic programming. Among the areas of application covered are mathematical economics, mathematical physics and biology, and aerospace, chemical, civil, electrical, and mechanical engineering.