Continuous and variable branching asymptotics

  • The regularity of solutions to elliptic equations on a manifold with singularities, say, an edge, can be formulated in terms of asymptotics in the distance variable r > 0 to the singularity. In simplest form such asymptotics turn to a meromorphic behaviour under applying the Mellin transform on the half-axis. Poles, multiplicity, and Laurent coefficients form a system of asymptotic data which depend on the specific operator. Moreover, these data may depend on the variable y along the edge. We then have y-dependent families of meromorphic functions with variable poles, jumping multiplicities and a discontinuous dependence of Laurent coefficients on y. We study here basic phenomena connected with such variable branching asymptotics, formulated in terms of variable continuous asymptotics with a y-wise discrete behaviour.

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Author:Mahdi Hedayat Mahmoudi, Bert-Wolfgang SchulzeGND, Liparit Tepoyan
ISSN:1662-9981 (print)
ISSN:1662-999X (online)
Parent Title (English):Journal of pseudo-differential operators and applications
Place of publication:Basel
Document Type:Article
Year of first Publication:2015
Year of Completion:2015
Release Date:2017/03/27
Tag:Asymptotics of solutions; Edge symbols; Weighted edge spaces
First Page:69
Last Page:112
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer Review:Referiert