On the univalence of solutions of second order elliptic equations in the unit disk on the plane
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 43, Tome 434 (2015), pp. 91-100
A. B. Zaitsev. On the univalence of solutions of second order elliptic equations in the unit disk on the plane. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 43, Tome 434 (2015), pp. 91-100. http://geodesic.mathdoc.fr/item/ZNSL_2015_434_a7/
@article{ZNSL_2015_434_a7,
     author = {A. B. Zaitsev},
     title = {On the univalence of solutions of second order elliptic equations in the unit disk on the plane},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {91--100},
     year = {2015},
     volume = {434},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_434_a7/}
}
TY  - JOUR
AU  - A. B. Zaitsev
TI  - On the univalence of solutions of second order elliptic equations in the unit disk on the plane
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2015
SP  - 91
EP  - 100
VL  - 434
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2015_434_a7/
LA  - ru
ID  - ZNSL_2015_434_a7
ER  - 
%0 Journal Article
%A A. B. Zaitsev
%T On the univalence of solutions of second order elliptic equations in the unit disk on the plane
%J Zapiski Nauchnykh Seminarov POMI
%D 2015
%P 91-100
%V 434
%U http://geodesic.mathdoc.fr/item/ZNSL_2015_434_a7/
%G ru
%F ZNSL_2015_434_a7

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Sufficient conditions on a function continuous on the unit circle are found ensuring that the solution of the Dirichlet problem in the unit disk for a certain second order partial differential equation with this boundary function is a homeomorphism of the unit disk onto a simply connected Jordan domain.

[1] G. C. Verchota, A. L. Vogel, “Nonsymmetric systems on nonsmooth planar domains”, Trans. Amer. Math. Soc., 349:11 (1997), 4501–4535 | DOI | MR | Zbl

[2] P. Duren, Harmonic mappings in the plane, Cambridge University Press, 2004 | MR | Zbl

[3] G. Alessandrini, V. Nesi, “Elliptic systems and material interpretation”, Funct. Approx. Comment. Math., 40:1 (2009), 105–115 | DOI | MR | Zbl

[4] A. B. Zaitsev, “Ob otobrazheniyakh resheniyami ellipticheskikh uravnenii vtorogo poryadka”, Matem. zametki, 95:5 (2014), 718–733 | DOI | Zbl

[5] I. I. Privalov, Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, M.–L., 1950