The Hot Spots Conjecture on a Class of Domains in R^n with n≥3

The Hot Spots Conjecture on a Class of Domains in R^n with n≥3

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摘要 In this paper, we define a class of domains in R^n. Using the synchronous coupling of reflecting Brownian motion, we obtain the monotonicity property of the solution of the heat equation with the Neumann boundary conditions. We then show that the hot spots conjecture holds for this class of domains. In this paper, we define a class of domains in R^n. Using the synchronous coupling of reflecting Brownian motion, we obtain the monotonicity property of the solution of the heat equation with the Neumann boundary conditions. We then show that the hot spots conjecture holds for this class of domains.

作者 Peng-fei YANG

机构地区 School of Science

出处《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2011年第4期639-646,共8页 应用数学学报（英文版）

关键词 synchronous coupling reflecting Brownian motion hot spots conjecture Neumann eigenfunctions synchronous coupling, reflecting Brownian motion, hot spots conjecture, Neumann eigenfunctions

分类号 O175.26 [理学—数学] O552.1 [理学—基础数学]

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Acta Mathematicae Applicatae Sinica

2011年第4期

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The Hot Spots Conjecture on a Class of Domains in R^n with n≥3

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