Asymptotic Parametrices of Elliptic Edge Operators

2010/10/07 by H. -J. Flad, Flad, H. -J., G. Harutyunyan +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1010.1453

Some typos and minor errors corrected

arxiv created 2011/03/01 · arxiv updated 2011/03/02

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.

Related

• Cone and edge calculus with discrete asymptotics
• The iterative Structure of Corner Operators
• The singular functions of branching edge asymptotics
• Parameter-dependent Edge Operators
• Degenerate operators on the half-line