Spectral Invariance of Pseudodifferential Boundary Value Problems on Manifolds with Conical Singularities

TL;DR

This paper proves spectral invariance for pseudodifferential boundary value problems on manifolds with conical singularities, extending classical results to a broader geometric setting and linking Fredholm property with ellipticity.

Contribution

It establishes spectral invariance in the Lp-setting for boundary value problems on singular manifolds, and connects Fredholm property with ellipticity in this context.

Findings

Spectral invariance holds for classical pseudodifferential boundary value problems on conical manifolds.

Spectral invariance extends to the Boutet de Monvel algebra with parameters.

Fredholm property is equivalent to ellipticity in these boundary value problems.

Abstract

We prove the spectral invariance of the algebra of classical pseudodifferential boundary value problems on manifolds with conical singularities in the Lp-setting. As a consequence we also obtain the spectral invariance of the classical Boutet de Monvel algebra of zero order operators with parameters. In order to establish these results, we show the equivalence of Fredholm property and ellipticity for both cases.