Abstract

Estimates for the ratio of the first two eigenvalues of the Dirichlet-Laplace operator with a drift

Highlights

  • We say that λ is an eigenvalue of problem (2) if there exists uλ ∈ X0 \ {0} such that

  • Function uλ from the above definition is called an eigenfunction corresponding to the eigenvalue λ

  • Using [2, relation (2.10) on page 715] (see [9, Theoreme 8.7] with H = X0 applied for the particular case induced by problem (2)), we deduce that the first eigenvalue of problem (2) has the following variational characterization λ1(Ω) := inf u∈X0 \{0}

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Summary

Introduction

The eigenvalue problem of the Dirichlet-Laplace operator The eigenvalue problem for the Dirichlet-Laplace operator on Ω reads as follows Denote by μ1(Ω) and μ2(Ω) the first two eigenvalues of problem (1). The eigenvalue problem of the Dirichlet-Laplace operator with a drift

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