Lower bounds for Dirichlet Laplacians and uncertainty principles

被引：5

作者：

Stollmann, Peter ^{[1
]}

Stolz, Guenter ^{[2
]}

机构：

[1] Tech Univ Chemnitz, Fak Math, D-09107 Chemnitz, Germany

[2] Univ Alabama Birmingham, Dept Math, 1402 10th Ave South, Birmingham, AL 35294 USA

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2021年 / 23卷 / 07期

关键词：

Uncertainty principle; Dirichlet Laplacians; unique continuation; LOCALIZATION; INEQUALITIES; CONTINUATION; CONVERGENCE; SCATTERING; MODEL;

D O I：

10.4171/JEMS/1055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove lower bounds for the Dirichlet Laplacian on possibly unbounded domains in terms of natural geometric conditions. This is used to derive uncertainty principles for low energy functions of general elliptic second order divergence form operators with not necessarily continuous main part.

引用

页码：2337 / 2360

页数：24

共 50 条

[31] Lower bounds for the first Dirichlet eigenvalue of the Laplacian for domains in hyperbolic space
Artamoshin, Sergei
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2016, 160 (02) : 191 - 208
[32] The boundary behavior of heat kernels of Dirichlet Laplacians
Zhang, QS
JOURNAL OF DIFFERENTIAL EQUATIONS, 2002, 182 (02) : 416 - 430
[33] ξ-determinants of Laplacians with Neumann and Dirichlet boundary conditions
Loya, P
Park, J
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2005, 38 (41): : 8967 - 8977
[34] THE DEVELOPMENT OF BIVARIATIONAL PRINCIPLES FOR THE CALCULATION OF UPPER AND LOWER BOUNDS
PACK, DC
ARCHIVES OF MECHANICS, 1982, 34 (03): : 275 - 285
[35] DEPTH LOWER BOUNDS IN STABBING PLANES FOR COMBINATORIAL PRINCIPLES
Dantchev, Stefan
Galesi, Nicola
Ghani, Abdul
Martin, Barnaby
LOGICAL METHODS IN COMPUTER SCIENCE, 2024, 20 (01)
[36] Spectral multipliers and wave equation for sub-Laplacians: lower regularity bounds of Euclidean type
Martini, Alessio
Mueller, Detlef
Golo, Sebastiano Nicolussi
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2023, 25 (03) : 785 - 843
[37] INTRINSIC ULTRACONTRACTIVITY OF DIRICHLET LAPLACIANS IN NONSMOOTH DOMAINS
CIPRIANI, F
POTENTIAL ANALYSIS, 1994, 3 (02) : 203 - 218
[38] PROPERTY OF BIHARMONIC FUNCTIONS WITH DIRICHLET FINITE LAPLACIANS
NAKAI, M
SARIO, L
MATHEMATICA SCANDINAVICA, 1971, 29 (02) : 307 - &
[39] Lower and upper bounds of Dirichlet eigenvalues for totally characteristic degenerate elliptic operators
CHEN Hua
QIAO RongHua
LUO Peng
XIAO DongYuan
Science China(Mathematics), 2014, 57 (11) : 2235 - 2246
[40] UPPER AND LOWER BOUNDS FOR THE NUMERICAL SOLUTION OF THE DIRICHLET DIFFERENCE BOUNDARY VALUE PROBLEM
DIAZ, JB
ROBERTS, RC
JOURNAL OF MATHEMATICS AND PHYSICS, 1952, 31 (03): : 184 - 191

← 1 2 3 4 5 →