For citation:
Prokhorov D. V., Zakharov A. M. Integrability of a Partial Case of the Lowner Equation. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2010, vol. 10, iss. 2, pp. 19-23. DOI: 10.18500/1816-9791-2010-10-2-19-23
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
18.01.2010
Full text:
(downloads: 191)
Language:
Russian
Heading:
UDC:
517.54
Integrability of a Partial Case of the Lowner Equation
Autors:
Prokhorov Dmitri Valentinovich, Saratov State University
Zakharov Andrei Mikhailovich, Saratov State University
Abstract:
We give a quadrature solution to the partial case of the Lowner¨ equation for the upper half-plane.
Key words:
References:
- L¨owner, K. Untersuchungen ¨uber schlichte konforme Abbildungen des Einheitskreises. I / K. L¨owner // Math. Ann. – 1923. – V. 89, № 1–2. – P. 103–121.
- Александров, И.А. Параметрические продолжения в теории однолистных функций / И.А. Александров. М.: Наука, 1976.
- Kager, W. Exact solutions for Loewner evolutions / W. Kager, B. Nienhuis, L.P. Kadanoff // J. Statist. Phys. – 2004. V. 115, № 3–4. – P. 805–822.
- Куфарев, П.П. Одно замечание об уравнении Л¨евнера / П.П. Куфарев // Докл. АН СССР. – 1947. – V. 57. – P. 751–754.
- Marshall, D. The L¨owner differential equation and slit mappings / D. Marshall, S. Rohde // J. Amer. Math. Soc. – 2005. – V. 18, № 4. – P. 763–778.
- Lind, J. A sharp condition for the L¨owner equation to generate slits / J. Lind // Ann. Acad. Sci. Fenn. Math. – 2005. – V. 30, № 1. – P. 143–158.
- Prokhorov, D. Singular and tangent slit solutions to the L¨owner equation / D. Prokhorov, A. Vasil’ev // Analysis and Mathematical Physics. Trends in Mathematics / Ed. B. Gustafsson, A. Vasil’ev. – Basel: Birkhauser, 2009. – P. 451–459.
- 1045 reads