Boundary value problems for elliptic wedge operators: the first order case

TL;DR

This paper explores boundary value problems for first-order elliptic wedge operators, introducing new analytical tools like trace bundles and an extended calculus for anisotropic regularity, with illustrative examples.

Contribution

It develops the notion of trace bundles and extends the Douglis-Nirenberg calculus to analyze first-order elliptic wedge operators.

Findings

Introduction of trace bundle concept

Extension of pseudodifferential calculus for anisotropic spaces

Analysis of boundary value problems for first-order wedge operators

Abstract

This note is a description of some of the results obtained by the authors in connection with the problem in the title. These, discussed following a summary of background material concerning wedge differential operators, consist of the notion of trace bundle, an extension of the Douglis-Nirenberg calculus to handle spaces of anisotropic varying regularity and associated pseudodifferential operators, and boundary value problems proper, the latter in the first order case. The concepts concerning the main results are illustrated with simple examples.