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Two new universal inequalities for Neumann eigenvalues of the Laplacian on a planar convex domain

Kei Funano

Abstract

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

Two new universal inequalities for Neumann eigenvalues of the Laplacian on a planar convex domain

Abstract

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

Paper Structure

This paper contains 4 sections, 9 theorems, 29 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proof of the Main Theorems
  4. An weaker inequality of (\ref{['univ']})

Key Result

Theorem 1.1

Let $\Omega$ be a planar bounded convex domain. Then for any $k\geq l$ we have

Theorems & Definitions (12)

  • Theorem 1.1
  • Theorem 1.2
  • Proposition 2.1: H
  • Theorem 2.2: F
  • Theorem 2.3: Payne–Weinberger, PW
  • Theorem 2.4: Kröger, Kr
  • Theorem 2.5: Kröger, Kr2
  • Theorem 2.6: Buser, B
  • proof : Proof of Theorem \ref{['MTHM']}
  • proof : Proof of Theorem \ref{['MTHM2']}
  • ...and 2 more