Elliptic theory of differential edge operators, II: boundary value problems

TL;DR

This paper advances the theory of elliptic differential operators with edge degeneracies by formulating boundary conditions and constructing parametrices, emphasizing the microlocal structure of solutions.

Contribution

It extends previous work by developing boundary value problem formulations and parametrix constructions for elliptic edge operators.

Findings

Established boundary condition frameworks for elliptic edge operators

Constructed parametrices with detailed microlocal analysis

Enhanced understanding of solution regularity and asymptotics

Abstract

This is a continuation of the first author's development of the theory of elliptic differential operators with edge degeneracies. That first paper treated basic mapping theory, focusing on semi-Fredholm properties on weighted Sobolev and H\"older spaces and regularity in the form of asymptotic expansions of solutions. The present paper builds on this through the formulation of boundary conditions and the construction of parametrices for the associated boundary problems. As before, the emphasis is on the geometric microlocal structure of the Schwartz kernels of parametrices and generalized inverses.