Nonsmooth Pseudodifferential Boundary Value Problems on Manifolds

TL;DR

This paper investigates nonsmooth pseudodifferential boundary value problems on manifolds, establishing invariance of nonsmooth Green operators under coordinate changes to ensure coordinate-independent definitions.

Contribution

It introduces a framework for nonsmooth Green operators within the Boutet de Monvel calculus that remains invariant under smooth coordinate transformations.

Findings

Nonsmooth Green operators are invariant under smooth coordinate transformations.

A coordinate-independent definition of nonsmooth boundary value problems is established.

The framework extends classical pseudodifferential calculus to nonsmooth contexts.

Abstract

We study pseudodifferential boundary value problems in the context of the Boutet de Monvel calculus or Green operators, with nonsmooth coefficients on smooth compact manifolds with boundary. In order to have a definition that is independent of the choice of (smooth) coordinates, we prove that nonsmooth Green operators are invariant under smooth coordinate transformations.