scholarly journals On the proof of Taylor’s conjecture in multiply connected domains

2022 ◽  
Vol 124 ◽  
pp. 107654
Daniel Faraco ◽  
Sauli Lindberg ◽  
David MacTaggart ◽  
Alberto Valli
2002 ◽  
Vol 9 (2) ◽  
pp. 367-382
Z. Samsonia ◽  
L. Zivzivadze

Abstract Doubly-connected and triply-connected domains close to each other in a certain sense are considered. Some questions connected with conformal and quasiconformal mappings of such domains are studied using integral equations.

1996 ◽  
Vol 19 (3) ◽  
pp. 581-586
E. M. E. Zayed

The purpose of this paper is to derive some interesting asymptotic formulae for spectra of arbitrary multiply connected bounded domains in two or three dimensions, linked with variation of positive distinct functions entering the boundary conditions, using the spectral function∑k=1∞{μk(σ1,…,σn)+P}−2asP→∞. Further results may be obtained.

2013 ◽  
Vol 30 (4) ◽  
pp. 441-455 ◽  
Everett Kropf ◽  
Xiaotian Yin ◽  
Shing-Tung Yau ◽  
Xianfeng David Gu

N. M. Patrikalakis ◽  
H. N. Gursoy

Abstract In this paper we develop a new interrogation method based on the medial axis transform to extract some important global shape characteristics from geometric representations. These shape characteristics include constrictions, maximum thickness points, and associated length scales; isolation of holes and their proximity information; and a set of topologically simple subdomains decomposing a complex domain. The algorithm we develop to compute the medial axis transform of planar multiply connected shapes with curved boundaries can automatically identify these characteristics. Higher level algorithms for generation of finite element meshes of planar multiply connected domains, adaptive triangulation and approximation of trimmed curved surface patches and other engineering applications using the medial axis transform are also discussed.

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