Geodesic
Some boundary value problems for the Cauchy--Riemann equation in half lens
Eurasian mathematical journal, Tome 9 (2018) no. 3, pp. 73-84.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this article, the boundary behaviour of the Schwarz-type operator on the half lens $\Omega$ will be discussed and the existence of boundary values at corner points is proved. Finally, two basic boundary value problems, namely, Dirichlet and Neumann problems for analytic functions and more generally the Dirichlet problem for the inhomogeneous Cauchy–Riemann equation in $\Omega$ is investigated. 
@article{EMJ_2018_9_3_a5,
     author = {N. Taghizadeh and V. Soltani Mohammadi},
     title = {Some boundary value problems for the {Cauchy--Riemann} equation in half lens},
     journal = {Eurasian mathematical journal},
     pages = {73--84},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2018_9_3_a5/}
}
TY  - JOUR
AU  - N. Taghizadeh
AU  - V. Soltani Mohammadi
TI  - Some boundary value problems for the Cauchy--Riemann equation in half lens
JO  - Eurasian mathematical journal
PY  - 2018
SP  - 73
EP  - 84
VL  - 9
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2018_9_3_a5/
LA  - en
ID  - EMJ_2018_9_3_a5
ER  - 
%0 Journal Article
%A N. Taghizadeh
%A V. Soltani Mohammadi
%T Some boundary value problems for the Cauchy--Riemann equation in half lens
%J Eurasian mathematical journal
%D 2018
%P 73-84
%V 9
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2018_9_3_a5/
%G en
%F EMJ_2018_9_3_a5
N. Taghizadeh; V. Soltani Mohammadi. Some boundary value problems for the Cauchy--Riemann equation in half lens. Eurasian mathematical journal, Tome 9 (2018) no. 3, pp. 73-84. http://geodesic.mathdoc.fr/item/EMJ_2018_9_3_a5/

[1] S.A. Abdymanapov, H. Begehr, G. Harutyunyan, A.B. Tungatarov, “Four boundary value problems for the Cauchy–Riemann equation in a quarter plane”, More Progresses in Analysis, Proc. 5th Intern. ISAAC Congress (Catania, Italy, 2005), eds. H. Begehr, F. Nicolosi, World Sci., Singapore, 2009, 1137–1147 | DOI | MR | Zbl

[2] S.A. Abdymanapov, H. Begehr, A.B. Tungatarov, “Some Schwarz problems in a quarter plane”, Evraziiskii Matematicheskii Zhurnal, 3 (2005), 22–35

[3] H. Begehr, “Boundary value problems in complex analysis. I; II”, Bol. Asoc. Math. Venezolana, 12:1 (2005), 65–85 | MR | Zbl

[4] H. Begehr, Complex analytic methods for partial differential equations: an introductory text, World Scientific, Singapore, 1994, 250 pp. | MR | Zbl

[5] H. Begehr, E.A. Gaertner, “Dirichlet problem for the inhomogeneous polyharmonic equation in the upper half plane”, Georg. Math. J., 14:1 (2007), 33–52 | MR | Zbl

[6] H. Begehr, G. Harytyunyan, “Complex boundary value problems in a quarter plane”, Proc. 13th Intern. Conf. Finite Infinite Dimensional Complex Anal. Appl., eds. Y. Wang et al., World. Sci., New Jersey, 2006, 1–10 | Zbl

[7] H. Begehr, G. Harutyunyan, “Robin boundary value problem for the Cauchy–Riemann operator”, Complex Variables. Theory Appl., 50:15 (2005), 1125–1136 | DOI | MR | Zbl

[8] H. Begehr, T. Vaitekhovich, “Schwarz problem in lens and lune”, Complex Var. Elliptic Equ., 59:1 (2014), 76–84 | DOI | MR | Zbl

[9] E. Gaertner, Basic complex boundary value problems in the upper half plane, Ph.D. thesis, FU Berlin, 2006 http://www.diss.fu-berlin.de/diss/receive/FUDISS-thesis-000000002129

[10] N. Taghizadeh, V. Soltani Mohammadi, M. Najand Foumani, “Schwarz boundary value problem in half lens and half lune”, Complex Var. Elliptic Equ., 2015 | DOI | MR

[11] T. Vaitsiakhovich, Boundary value problems for complex partial differential equations in a ring domain, Ph.D. thesis, FU Berlin, 2008 http://www.diss.fu-berlin.de/diss/receive/FUDISS-thesis-000000003859

[12] T. Vaitekhovich, “Boundary value problems to first order complex partial differential equations in a ring domain”, Integral Transf. Special Funct., 19 (2008), 211–233 | DOI | MR | Zbl

[13] Y. Wang, “Schwarz-type boundary value problems for the polyanalytic equation in the half unit disc”, Complex Var. Elliptic Equ., 57:9 (2012), 983–993 | DOI | MR | Zbl