Sharp boundary estimates for elliptic operators

1998/09/29 by E. B. Davies, E B Davies, Davies, E B
Mathematics · Physics and Astronomy · #35P20 #35P99 #47A75 #47B25 #Advanced Harmonic Analysis Research #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:35P20 #msc:35P99 #msc:47A75 #msc:47B25

paper · pdf · doi:10.48550/arxiv.math/9809171

arxiv created 1998/09/29 · openalex publication_date 1998/09/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove sharp L² boundary decay estimates for the eigenfunctions of certain second order elliptic operators acting in a bounded region, and of their first order space derivatives, using only the Hardy inequality. We then deduce bounds on the change of the eigenvalues when the region is reduced slightly in size, subject to DBCs.

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