A General Class of Problems in Conformal Mapping

A General Class of Problems in Conformal Mapping.

belongs to class S if f(z) is regular and schlicht in zI < 1 and a, = 1. Let R be a closed set lying in zj < 1, and let *,1,(r) be a measure function defined in the space R. Given an integer n there is a number M M. such that If()-(z) < M for all z C R and for v = O, 1, 2, ..., n when f(z) belongs to class S. Let F,(ro Ro, ..., rny ) denote a complex-valued function which is continuous together...

Remarks on "some Problems in Conformal Mapping"

1. The present note contains several remarks on an earlier paper by the author [2].1 In Chapter IV, §4, which deals with the question of when we can have equality of modules for a triply-connected domain and a proper subdomain, the last sentence was added in proof. This accounts for the apparent disparity between it and the preceding one. In order to justify this statement we observe first that...

A General Theorem on Conformal Mapping of Multiply Connected Domains.

Another Remark on "some Problems in Conformal Mapping"

In a great many cases the methods used in the proofs of the above theorems can be used to determine whether a given continuum is a Wn set. In particular, they can be used to prove that no W-¡ set, M, has a complementary domain whose boundary, /, contains three limit points of B(M) — J, no Wi set has a complementary domain whose boundary contains five such points, and that there exists a Wo set ...

UNIQUENESS OF SOLUTION FOR A CLASS OF STEFAN PROBLEMS

This paper deals with a theoretical mathematical analysis of one-dimensional solidification problem, in which kinetic undercooling is incorporated into the This temperature condition at the interface. A model problem with nonlinear kinetic law is considered. We prove a local result intimate for the uniqueness of solution of the corresponding free boundary problem.