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

作　　者：Peng-fei YANG 

机构地区：[1]School of Science, Beijing Institute of Technology, Beijing 100081, China

出　　处：《Acta Mathematicae Applicatae Sinica》2011年第4期639-646,共8页应用数学学报（英文版）

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.

关 键 词：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]