Bounded H_\infty-calculus for pseudodifferential Douglis-Nirenberg systems of mild regularity

TL;DR

This paper establishes that parameter-ellipticity ensures a bounded H_infinity-calculus for pseudodifferential Douglis-Nirenberg systems with mild regularity, extending to non-pseudodifferential perturbations and applications in thermoelastic systems.

Contribution

It proves the bounded H_infinity-calculus for systems with mild regularity and non-pseudodifferential perturbations, broadening the scope of elliptic operator theory.

Findings

Parameter-ellipticity implies bounded H_infinity-calculus

Results apply to systems with Hoelder regularity coefficients

Applications include generalized thermoelastic plate equations

Abstract

Parameter-ellipticity with respect to a closed subsector of the complex plane for pseudodifferential Douglis-Nirenberg systems is discussed and shown to imply the existence of a bounded H_\infty-calculus in suitable scales of Sobolev, Besov, and Hoelder spaces. We also admit non pseudodifferential perturbations. Applications concern systems with coefficients of mild Hoelder regularity and the generalized thermoelastic plate equations.