Resolvents of elliptic cone operators

DOI10.1016/j.jfa.2006.07.010zbMath1109.58023arXivmath/0410176OpenAlexW2084573184MaRDI QIDQ860795

Thomas Krainer, Juan B. Gil, Gerardo A. Mendoza

Publication date: 9 January 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0410176

zbMATH Keywords

elliptic boundary value problemselliptic differential operators

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Pseudodifferential and Fourier integral operators on manifolds (58J40) Boundary value problems on manifolds (58J32)

Related Items (28)

On the domain of Dirac and Laplace type operators on stratified spaces ⋮ Smoothness and long time existence for solutions of the Cahn-Hilliard equation on manifolds with conical singularities ⋮ Zeta Functions of Elliptic Cone Operators ⋮ A Polyakov formula for sectors ⋮ Elliptic boundary problems on manifolds with polycylindrical ends ⋮ Conic manifolds under the Yamabe flow ⋮ Spectral invariance of pseudodifferential boundary value problems on manifolds with conical singularities ⋮ The fractional porous medium equation on manifolds with conical singularities II ⋮ Resolvents and complex powers of semiclassical cone operators ⋮ Heat kernel coefficients for Laplace operators on the spherical suspension ⋮ Bounded imaginary powers of cone differential operators on higher order Mellin-Sobolev spaces and applications to the Cahn-Hilliard equation ⋮ Complex powers for cone differential operators and the heat equation on manifolds with conical singularities ⋮ Exotic expansions and pathological properties of \(\zeta\)-functions on conic manifolds ⋮ A conic manifold perspective of elliptic operators on graphs ⋮ Bounded \(H_\infty\)-calculus for cone differential operators ⋮ Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone ⋮ Resolvents of cone pseudodifferential operators, asymptotic expansions and applications ⋮ Trace expansions for elliptic cone operators with stationary domains ⋮ On the completeness of the generalized eigenfunctions of elliptic operators on manifolds with conical singularities ⋮ Spectral properties of reducible conical metrics ⋮ Edge quantisation of elliptic operators ⋮ Existence and maximalL^p-regularity of solutions for the porous medium equation on manifolds with conical singularities ⋮ The harmonic map heat flow on conic manifolds ⋮ The determinant on flat conic surfaces with excision of disks ⋮ The Swift-Hohenberg equation on conic manifolds ⋮ Analysis of periodic Schrödinger operators: Regularity and approximation of eigenfunctions ⋮ BoundedH_∞-Calculus for Differential Operators on Conic Manifolds with Boundary ⋮ Resolvents of Elliptic Boundary Problems on Conic Manifolds

Cites Work

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• The expansion of the resolvent near a singular stratum of conical type
• Cone pseudodifferential operators in the edge symbolic calculus
• Heat kernel asymptotics on manifolds with conic singularities
• On the resolvent of differential operators on conic manifolds
• Geometry and Spectra of Closed Extensions of Elliptic Cone Operators
• On the spectral geometry of spaces with cone-like singularities
• Differential operators of Fuchs type, conical singularities, and asymptotic methods
• Adjoints of elliptic cone operators
• Full asymptotic expansion of the heat trace for non–self–adjoint elliptic cone operators
• The Resolvent of Closed Extensions of Cone Differential Operators

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