具有小 Dirichet 区域的混合特征值问题的热点定理

arXiv - MATH - Spectral Theory Pub Date : 2024-09-05 DOI:arxiv-2409.03908

Lawford Hatcher

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摘要

我们证明，在凸域上，如果 Dirichlet 区域连通且足够小，则第一混合拉普拉斯特征函数没有内部临界点。我们利用这一结果构造了一个新的多边形域族，对这些域，Rauch 的热点猜想成立，并证明了一个关于热点猜想的新的一般定理。

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A hot spots theorem for the mixed eigenvalue problem with small Dirichet region

We prove that on convex domains, first mixed Laplace eigenfunctions have no interior critical points if the Dirichlet region is connected and sufficiently small. We use this result to construct a new family of polygonal domains for which Rauch's hot spots conjecture holds and to prove a new general theorem regarding the hot spots conjecture.

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arXiv - MATH - Spectral Theory

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