Asymptotic Parametrices of Elliptic Edge Operators

TL;DR

This paper develops a new approach to analyze solutions of elliptic equations near singularities on manifolds with edges, using asymptotic parametrices with flat remainders, inspired by models in particle physics.

Contribution

It introduces a novel method for constructing asymptotic parametrices for elliptic edge operators, advancing the understanding of solutions near singularities.

Findings

Construction of asymptotic parametrices with flat remainders

Application to models with embedded singularities in particle physics

Enhanced analysis of elliptic equations on singular manifolds

Abstract

We study operators on a singular manifold, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. The idea is to construct so-called asymptotic parametrices with flat left -over terms. Our structures are motivated by models of particle physics with singular potentials that contribute embedded singularities in $\R^N$ of higher order, according to the number of particles.