Generalized condensers and distortion theorems for conformal mappings of planar domains

2007 ◽  
pp. 33-51 ◽  
Author(s):  
V. N. Dubinin ◽  
D. B. Karp
Keyword(s):  
Conformal Mappings ◽  
Planar Domains ◽  
Distortion Theorems

A boundary estimate for harmonic functions

1982 ◽  
Vol 91 (1) ◽  
pp. 79-90 ◽  
Author(s):  
P. J. Rippon
Keyword(s):  
Euclidean Space ◽  
Harmonic Functions ◽  
Conformal Mappings ◽  
Dimensional Euclidean Space ◽  
Boundary Behaviour ◽  
Boundary Estimate ◽  
Distortion Theorems

In this paper we extend to certain domains in m-dimensional Euclidean space Rm, m ≥ 3, some results about the boundary behaviour of harmonic functions which, in R2, are known to follow from distortion theorems for conformal mappings.

scholarly journals Sharp Estimates for Green’s Functions of Cone-Type Planar Domains

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Mohamed Amine Ben Boubaker ◽  
Mohamed Selmi
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Conformal Mappings ◽  
Sharp Estimates ◽  
Planar Domains ◽  
Cone Type

We establish sharp estimates for Green’s functions of cone-type planar domains. Our work generalizes all estimates given by Zhao in 1988 and Selmi in 2000. Our principal idea is to use conformal mappings.

scholarly journals Euler Equations on General Planar Domains

Annals of PDE ◽  
2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Zonglin Han ◽  
Andrej Zlatoš
Keyword(s):  
Euler Equations ◽  
Planar Domains

scholarly journals Polyanalytic boundary value problems for planar domains with harmonic Green function

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Heinrich Begehr ◽  
Bibinur Shupeyeva
Keyword(s):  
Green Function ◽  
Boundary Value Problems ◽  
Arbitrary Order ◽  
Boundary Value ◽  
Planar Domains ◽  
Schwarz Problem ◽  
Bianalytic Functions ◽  
Neumann Type ◽  
The Neumann Problem ◽  
Well Posed

AbstractThere are three basic boundary value problems for the inhomogeneous polyanalytic equation in planar domains, the well-posed iterated Schwarz problem, and further two over-determined iterated problems of Dirichlet and Neumann type. These problems are investigated in planar domains having a harmonic Green function. For the Schwarz problem, treated earlier [Ü. Aksoy, H. Begehr, A.O. Çelebi, AV Bitsadze’s observation on bianalytic functions and the Schwarz problem. Complex Var Elliptic Equ 64(8): 1257–1274 (2019)], just a modification is mentioned. While the Dirichlet problem is completely discussed for arbitrary order, the Neumann problem is just handled for order up to three. But a generalization to arbitrary order is likely.

scholarly journals Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1035
Author(s):  
Cai-Mei Yan ◽  
Rekha Srivastava ◽  
Jin-Lin Liu
Keyword(s):  
Difference Operator ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Sufficient And Necessary Conditions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

scholarly journals Asymptotic behaviour of optimal spectral planar domains with fixed perimeter

2013 ◽  
Vol 54 (5) ◽  
pp. 053504 ◽  
Author(s):  
Dorin Bucur ◽  
Pedro Freitas
Keyword(s):  
Asymptotic Behaviour ◽  
Planar Domains
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