Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Riesz means asymptotics for Dirichlet and Neumann Laplacians on Lipschitz domains
View through CrossRef
Abstract
We consider the eigenvalues of the Dirichlet and Neumann Laplacians on a bounded domain with Lipschitz boundary and prove two-term asymptotics for their Riesz means of arbitrary positive order. Moreover, when the underlying domain is convex, we obtain universal, non-asymptotic bounds that correctly reproduce the two leading terms in the asymptotics and depend on the domain only through simple geometric characteristics. Important ingredients in our proof are non-asymptotic versions of various Tauberian theorems.
Title: Riesz means asymptotics for Dirichlet and Neumann Laplacians on Lipschitz domains
Description:
Abstract
We consider the eigenvalues of the Dirichlet and Neumann Laplacians on a bounded domain with Lipschitz boundary and prove two-term asymptotics for their Riesz means of arbitrary positive order.
Moreover, when the underlying domain is convex, we obtain universal, non-asymptotic bounds that correctly reproduce the two leading terms in the asymptotics and depend on the domain only through simple geometric characteristics.
Important ingredients in our proof are non-asymptotic versions of various Tauberian theorems.
Related Results
Persistent Topological Laplacians -- a Survey
Persistent Topological Laplacians -- a Survey
Persistent topological Laplacians constitute a new class of tools in topological data analysis (TDA), motivated by the necessity to address challenges encountered in persistent hom...
Transport laplacien, problème inverse et opérateurs de Dirichlet-Neumann
Transport laplacien, problème inverse et opérateurs de Dirichlet-Neumann
Le travail de ma thèse est basé sur ces 4 points : i) Transport laplacien d'une cellule absorbante : Soit un certain espèce (cellule) de concentration C(x), qui diffuse dans un mil...
Compactness of Commutators for Riesz Potential on Local Morrey-type spaces
Compactness of Commutators for Riesz Potential on Local Morrey-type spaces
The paper considers Morrey-type local spaces from LMpθw The main work is the proof of the commutator compactness theorem for the Riesz potential [b,Iα] in local Morrey-type spaces ...
Mild Riesz* homomorphisms of higher degrees
Mild Riesz* homomorphisms of higher degrees
Abstract
Riesz* homomorphisms on ordered vector spaces are characterized, intrinsically, via a condition on finite sets. As it is not suffici...
The research of $({\rm{G}}, {\rm{w}})$-Chaos and G-Lipschitz shadowing property
The research of $({\rm{G}}, {\rm{w}})$-Chaos and G-Lipschitz shadowing property
<abstract>
<p>In this paper, we introduce the concepts of $ (G, w) - $ Chaos and $ G - $ Lipschitz shadowing property. We study the dynamical properties of $ (G, w) - ...
Minimal lipschitz extension
Minimal lipschitz extension
Extensions lipschitziennes minimales
Cette thèse est consacrée aux quelques problèmes mathématiques concernant les extensions minimales de Lipschitz. Elle est organ...
Well-Posedness of the Fisher–KPP Equation with Neumann, Dirichlet, and Robin Boundary Conditions on the Real Half Line
Well-Posedness of the Fisher–KPP Equation with Neumann, Dirichlet, and Robin Boundary Conditions on the Real Half Line
We consider the Fisher–KPP equation with Neumann boundary conditions on the real half line. We claim that the Fisher-KPP equation with Neumann boundary conditions is well-posed onl...
Well-Posedness of the Fisher–KPP Equation with Neumann, Dirichlet, and Robin Boundary Conditions on the Real Half Line
Well-Posedness of the Fisher–KPP Equation with Neumann, Dirichlet, and Robin Boundary Conditions on the Real Half Line
We consider the Fisher–KPP equation with Neumann boundary conditions on the real half line. We claim that the Fisher-KPP equation with Neumann boundary conditions is well-posed onl...