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.
| Author details: | Mahdi Hedayat MahmoudiORCiD, Bert-Wolfgang SchulzeGND, Liparit Tepoyan |
|---|---|
| DOI: | https://doi.org/10.1007/s11868-015-0110-3 |
| ISSN: | 1662-9981 |
| ISSN: | 1662-999X |
| Title of parent work (English): | Journal of pseudo-differential operators and applications |
| Publisher: | Springer |
| Place of publishing: | Basel |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2015 |
| Publication year: | 2015 |
| Release date: | 2017/03/27 |
| Tag: | Asymptotics of solutions; Edge symbols; Weighted edge spaces |
| Volume: | 6 |
| Issue: | 1 |
| Number of pages: | 44 |
| First page: | 69 |
| Last Page: | 112 |
| Funding institution: | DAAD |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
