Bounded ${\mathbf{H}}_{\infty }$-Calculus for Differential Operators on Conic Manifolds with Boundary

Abstract

We derive conditions that ensure the existence of a bounded $H_{\infty }$-calculus in weighted $L_p$-Sobolev spaces for closed extensions ${\underline{A}}_T$ of a differential operator $A$ on a conic manifold with boundary, subject to differential boundary conditions $T$. In general, these conditions ask for a particular pseudodifferential structure of the resolvent $(\lambda -{\underline{A}}_T{)}^{-1}$ in a sector $\Lambda \subset \mathbf{C}$. In case of the minimal extension they reduce to parameter-ellipticity of the boundary value problem $(A,T)$. Examples concern the Dirichlet and Neumann Laplacians.

23 pages

References in corpus (5)

• Bounded Imaginary Powers of Differential Operators on Manifolds with Conical Singularities
• Realizations of Differential Operators on Conic Manifolds with Boundary
• Resolvents of elliptic boundary problems on conic manifolds
• Resolvents of elliptic cone operators
• Geometry and spectra of closed extensions of elliptic cone operators

Cited by in corpus (9)

• Anisotropic Function Spaces on Singular Manifolds
• Singular parabolic equations of second order on manifolds with singularities
• Bounded $H_{\infty }$-calculus for cone differential operators
• The ubiquitous $\zeta$-function and some of its "usual" and "unusual" meromorphic properties
• Maximal $L_p$-regularity of non-local boundary value problems
• Function Spaces on Uniformly Regular and Singular Riemannian Manifolds
• Bounded H_\infty-calculus for pseudodifferential Douglis-Nirenberg systems of mild regularity
• $H_{\infty }$-calculus for Hypoelliptic Pseudodifferential Operators
• Bounded $H_{\infty }$-calculus for Boundary Value Problems on Manifolds with Conical Singularities