Bounded $H_{\infty }$-calculus for Boundary Value Problems on Manifolds with Conical Singularities

Abstract

Realizations of differential operators subject to differential boundary conditions on manifolds with conical singularities are shown to have a bounded $H_{\infty }$-calculus in appropriate $L_p$-Sobolev spaces provided suitable conditions of parameter-ellipticity are satisfied. Applications concern the Dirichlet and Neumann Laplacian and the porous medium equation.

31 pages

References in corpus (2)

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