The Resolvent of Closed Extensions of Cone Differential Operators

2002/09/27 by Elmar Schrohe, Schrohe, Elmar, Joerg Seiler +1 · 1 citation
Mathematics · #35J70 #47A10 #58J40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory in Mathematical Physics #math.AP #msc:35J70 #msc:47A10 #msc:58J40

paper · pdf · doi:10.48550/arxiv.math/0209381

29 pages

arxiv created 2002/09/27 · openalex publication_date 2002/09/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study closed extensions A of an elliptic differential operator on a manifold with conical singularities, acting as an unbounded operator on a weighted L_p-space. Under suitable conditions we show that the resolvent (λ-A)^-1 exists in a sector of the complex plane and decays like 1/|λ| as |λ| tends to infinity. Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of A. As an application we treat the Laplace-Beltrami operator for a metric with straight conical degeneracy and describe domains yielding maximal regularity for the Cauchy problem u-Δu=f, u(0)=0.

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• Evolution Equations on Manifolds with Conical Singularities

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