On the Differentiability of Conformal Maps at the Boundary

Content Provider	Scilit
Author	Eke, B. G.
Copyright Year	1971
Description	Let S be a simply connected domain in the w + u + iv plane and let ∂S denote its boundary which we assume passes through w= ∞. Suppose that the segment L= {u ≧ $u_{0}$; v = 0} of the real axis lies in S and that $w_{∞}$ is the point of ∂ S accessible along L. Let z = z(w) = x(w) + iy(w) map S in a (1 — 1) conformal way onto ∑ = {z = x + iy: — ∞ < x < + ∞ } so that . The inverse map is w = w(z) = u(z) + iv(z). S is said to possess a finite angular derivative at w∞ if z(w) — w approaches a finite limit (called the angular derivative) as $w→w_{∞}$ in certain substrips of S.
Related Links	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/E590263931D354A81AA485EE2505964B/S0027763000014045a.pdf/div-class-title-on-the-differentiability-of-conformal-maps-at-the-boundary-a-href-fn01-ref-type-fn-span-class-sup-1-span-a-div.pdf
Ending Page	53
Page Count	11
Starting Page	43
ISSN	00277630
e-ISSN	21526842
DOI	10.1017/s0027763000014045
Journal	Nagoya Mathematical Journal
Volume Number	41
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	1971-02-01
Access Restriction	Open
Subject Keyword	Nagoya Mathematical Journal Mathematical Physics Differentiability
Content Type	Text
Resource Type	Article
Subject	Mathematics