Resolvents of elliptic boundary problems on conic manifolds

TL;DR

This paper extends the analysis of elliptic operator resolvents on conic manifolds to those with boundaries, establishing sectors of minimal growth and clarifying the resolvent's analytic structure under boundary conditions.

Contribution

It introduces new results on the existence of sectors of minimal growth for boundary value problems on conic manifolds with boundary, under natural ellipticity conditions.

Findings

Proves existence of sectors of minimal growth for boundary value problems

Clarifies the analytic structure of the resolvent for cone operators

Extends previous work to manifolds with boundary

Abstract

This paper is a continuation of the investigation of resolvents of elliptic operators on conic manifolds from math.AP/0410178 and math.AP/0410176 to the case of manifolds with boundary and realizations of operators under boundary conditions. We prove the existence of sectors of minimal growth for realizations of boundary value problems for cone operators under natural ellipticity conditions on the symbols. Special attention is devoted to the clarification of the analytic structure of the resolvent.