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A note on the distribution of Neumann eigenvalues of the Laplacian on a Euclidean convex domain

Kei Funano

Abstract

We establish two universal inequalities for Neumann eigenvalues of the Laplacian on a Euclidean convex domain.

A note on the distribution of Neumann eigenvalues of the Laplacian on a Euclidean convex domain

Abstract

We establish two universal inequalities for Neumann eigenvalues of the Laplacian on a Euclidean convex domain.
Paper Structure (3 sections, 8 theorems, 28 equations)

This paper contains 3 sections, 8 theorems, 28 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proof of the Main Theorem

Key Result

Theorem 1.1

There exists a universal numeric constant $c>0$ which satisfies the following. Let $\Omega$ be a bounded convex domain in $\mathbb{R}^n$. Then for any $k\geq l$ we have

Theorems & Definitions (11)

  • Theorem 1.1
  • Proposition 2.1: H
  • Theorem 2.2: F
  • Theorem 2.3: Payne–Weinberger, PW
  • Theorem 2.4: Kröger, Kr2
  • Theorem 2.5: Buser, B
  • Lemma 3.1
  • Lemma 3.2
  • proof : Proof of Theorem \ref{['MTHM']}
  • proof : Proof of Lemma \ref{['Mlem1']}
  • ...and 1 more