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

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