Boutet de Monvel operators on singular manifolds

TL;DR

This paper develops a Boutet de Monvel calculus for boundary value problems on Lie manifolds with boundary, broadening the analytical tools available for singular and non-compact manifolds.

Contribution

It introduces a new calculus framework for pseudodifferential boundary value problems on Lie manifolds with boundary, extending existing methods to more general singular manifolds.

Findings

Constructed a Boutet de Monvel calculus for Lie manifolds with boundary.

Extended pseudodifferential boundary problem analysis to non-compact, singular manifolds.

Provided a modeling approach for various classes of singular manifolds.

Abstract

We construct a Boutet de Monvel calculus for general pseudodifferential boundary value problems defined on a broad class of non-compact manifolds, the class of so-called Lie manifolds with boundary. It is known that this class of non-compact manifolds can be used to model many classes of singular manifolds.