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

## TL;DR

This paper establishes conditions under which differential operators on manifolds with conical singularities have a bounded $H_{
abla}$-calculus, enabling advanced analysis of boundary value problems with applications to Laplacians and porous medium equations.

## Contribution

It proves bounded $H_{
abla}$-calculus for differential operators on manifolds with conical singularities under parameter-ellipticity conditions, extending functional calculus theory.

## Key findings

- Bounded $H_{
abla}$-calculus established for operators on singular manifolds
- Applications to Dirichlet and Neumann Laplacians demonstrated
- Analysis of porous medium equation on conical manifolds provided

## 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.