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.

中文翻译：

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有界H _{∞ -}锥形奇点流形上边值问题的演算

受微分边界条件约束的微分算子在具有圆锥奇点的流形上的实现被证明具有有界 $H_{\infty }$- 适当的微积分 ${升}_{磷}$-Sobolev 空间提供了满足参数椭圆度的合适条件。应用涉及 Dirichlet 和 Neumann Laplacian 以及多孔介质方程。