IUMJ

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

Authors: Rafe Mazzeo and Boris Vertman

Issue: Volume 63 (2014), Issue 6, 1911-1955

Abstract:

This is a continuation of the first author's development [R. Mazzeo, \textit{Elliptic theory of differential edge operators. I}, Comm. Partial Differential Equations \textbf{16} (1991), no. 10, 1615--1664] 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 in [R. Mazzeo, \textit{Elliptic theory of differential edge operators. I}, Comm. Partial Differential Equations \textbf{16} (1991), no. 10, 1615--1664], the emphasis is on the geometric microlocal structure of the Schwartz kernels of parametrices and generalized inverses.