第二个非平凡Neumann特征值的最大化

IF 5.4 3区材料科学 Q2 CHEMISTRY, PHYSICAL

ACS Applied Energy Materials Pub Date : 2018-01-23 DOI:10.4310/ACTA.2019.V222.N2.A2

D. Bucur, A. Henrot

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引用次数: 30

摘要

本文证明了在给定测度为m的rn光滑域上拉普拉斯算子的第二(非平凡)Neumann特征值在两个测度为m2的不相交球的并集上达到最大值。因此，诺伊曼特征值的P{\'o}lya猜想对第二个特征值和任意域都成立。此外，我们还证明了在非光滑域和非光滑密度的情况下，相同不等式的松弛形式成立。

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Maximization of the second non-trivial Neumann eigenvalue

In this paper we prove that the second (non-trivial) Neumann eigenvalue of the Laplace operator on smooth domains of R N with prescribed measure m attains its maximum on the union of two disjoint balls of measure m 2. As a consequence, the P{\'o}lya conjecture for the Neumann eigenvalues holds for the second eigenvalue and for arbitrary domains. We moreover prove that a relaxed form of the same inequality holds in the context of non-smooth domains and densities.

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来源期刊

ACS Applied Energy Materials Materials Science-Materials Chemistry

CiteScore

10.30

自引率

6.20%

发文量

1368

期刊介绍： ACS Applied Energy Materials is an interdisciplinary journal publishing original research covering all aspects of materials, engineering, chemistry, physics and biology relevant to energy conversion and storage. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important energy applications.