关于平面上的 $\infty$-ground 状态

IF 0.6 3区数学 Q3 MATHEMATICS

Mathematical Research Letters Pub Date : 2024-05-14 DOI:10.4310/mrl.2023.v30.n5.a11

Erik Lindgren, Peter Lindqvist

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引用次数: 0

摘要

我们研究平面凸域中的＄\infty＄-Ground状态。在多边形中，$\infty$-Ground 状态不满足 $\infty$-Laplace 方程的点是有特征的：它们被限制在特定的曲线上，这些曲线就像吸引（虚构的）流线。在这些曲线之外梯度是连续的，没有流线可以在那里相遇。

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On $\infty$-ground states in the plane

We study $\infty$-Ground states in convex domains in the plane. In a polygon, the points where an $\infty$-Ground state does not satisfy the $\infty$-Laplace Equation are characterized: they are restricted to lie on specific curves, which are acting as attracting (fictitious) streamlines. The gradient is continuous outside these curves and no streamlines can meet there.

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来源期刊

Mathematical Research Letters 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

6.0 months

期刊介绍： Dedicated to publication of complete and important papers of original research in all areas of mathematics. Expository papers and research announcements of exceptional interest are also occasionally published. High standards are applied in evaluating submissions; the entire editorial board must approve the acceptance of any paper.