Absence of L^p spectrum for asymptotically flat diffusions in region with cavities

2025/07/14 by Agnid Banerjee, Nicola Garofalo, Banerjee, Agnid +1 · 1 citation
Computer Science · Mathematics · #35P15 #35Q40 #47A75 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2507.10728

openalex publication_date 2025/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study solutions to variable-coefficient elliptic equations of the form -\D(A(x) ∇ u) = κu, κ>0, in an exterior domain \Om⊂ \Rn, where A(x) is uniformly elliptic and asymptotically flat. Extending Rellich's classical L² result for the Laplacian, we show that if u∈ L^p(\Om) for some 0

Citations

• A Rellich type estimate for a subelliptic Helmholtz equation with mixed homogeneities
• An observation on eigenfunctions of the Laplacian
• Carleman estimates for Baouendi-Grushin operators with applications to quantitative uniqueness and strong unique continuation

Cited by

• On Rellich-type asymptotics for eigenfunctions on rank one symmetric spaces of noncompact type

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