Critical heat kernel estimates via Hardy-Sobolev inequalities

2003/02/26 by G. Barbatis, Gerassimos Barbatis, Barbatis, G. +6
Computer Science · Mathematics · #35B05 (Secondary) #35K20 #35K65 (Primary) 26D10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Spectral Theory (math.SP) #math.AP #math.SP #msc:26D10 #msc:35B05 #msc:35K20 #msc:35K65

paper · pdf · doi:10.48550/arxiv.math/0302331

23 pages

arxiv created 2003/02/26 · openalex publication_date 2003/02/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain Sobolev inequalities for the Schrodinger operator -Δ-V, where V has critical behaviour V(x)=((N-2)/2)²|x|^-2 near the origin. We apply these inequalities to obtain pointwise estimates on the associated heat kernel, improving upon earlier results.

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