热点常数的上界

IF 1.3 2区数学 Q1 MATHEMATICS

Revista Matematica Iberoamericana Pub Date : 2021-06-07 DOI:10.4171/rmi/1350

S. Steinerberger

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引用次数: 4

摘要

设D⊂R是具有光滑边界的有界连通域，设-∆u=μ1u是具有Neumann边界条件的拉普拉斯算子的第一个非平凡本征函数。我们证明了‖u‖L∞（D）≤60。这表明热点猜想不可能因任意因素而失败。Kleefeld的一个例子表明，最佳常数至少为1+10−3。

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An upper bound on the hot spots constant

Let D ⊂ R be a bounded, connected domain with smooth boundary and let −∆u = μ1u be the first nontrivial eigenfunction of the Laplace operator with Neumann boundary conditions. We prove ‖u‖L∞(D) ≤ 60 · ‖u‖L∞(∂D). This shows that the Hot Spots Conjecture cannot fail by an arbitrary factor. An example of Kleefeld shows that the optimal constant is at least 1 + 10−3.

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来源期刊

Revista Matematica Iberoamericana 数学-数学

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Revista Matemática Iberoamericana publishes original research articles on all areas of mathematics. Its distinguished Editorial Board selects papers according to the highest standards. Founded in 1985, Revista is a scientific journal of Real Sociedad Matemática Española.