BOUNDS FOR EXIT TIMES OF BROWNIAN MOTION AND THE FIRST DIRICHLET EIGENVALUE FOR THE LAPLACIAN

被引：0

作者：

Banuelos, Rodrigo ^{[1
]}

Mariano, Phanuel ^{[2
]}

Wang, Jing ^{[1
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Union Coll, Dept Math, Schenectady, NY 12308 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 376卷 / 08期

基金：

美国国家科学基金会;

关键词：

Exit times; moments; torsion function; Dirichlet Laplacian; principal eigenvalue; extremals; HOT-SPOTS CONJECTURE; TORSIONAL RIGIDITY; SPECTRAL GAP; INEQUALITIES; MOMENTS; EIGENFUNCTIONS; DIFFUSIONS;

D O I：

10.1090/tran/8903

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For domains in Rd, d > 2, we prove universal upper and lower bounds on the product of the bottom of the spectrum for the Laplacian to the power p > 0 and the supremum over all starting points of the p-moments of the exit time of Brownian motion. It is shown that the lower bound is sharp for integer values of p and that for p > 1, the upper bound is asymptotically sharp as d -> infinity. For all p > 0, we prove the existence of an extremal domain among the class of domains that are convex and symmetric with respect to all coordinate axes. For this class of domains we conjecture that the cube is extremal.

引用

页码：5409 / 5432

页数：24

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