Direct-Approximative methods for the numerical solution of the singular integro-differential equations in Holder spaces. (case when g ¹ 0)
by
Iurie Caraus
Moldova State University, Department of Mathematics and Informatics, Mateevici 60, str., Chisinau, Modova, MD-2009

Let \Gamma be a smooth Jordan border limiting the one-spanned area F⁺, containing a point t=0, F^-=C\{F⁺ \cup \Gamma}. Let z=\psi(w) be a function, mapping conformably and unambiguously the border {|w| > 1} on the surface F^-, so that \psi(\infty)=\infty, \psi^(')(\infty) > 0. We denote H_\beta(\Gamma) the complex spaces of functions satisfying on \Gamma the Hölder condition with some exponent \beta (0 < \beta < 1) with norm || g||_\beta = || g|| _C+H(g;\beta),

H(g, \beta) = \undersett' =/= t'' sup  | g(t'')-g(t')| | t'-t''|\beta ,    t', t'' in \Gamma.

We shall consider that function g(t) belongs to class H_\beta^q(\Gamma), q = 0, 1, ..., if it has derivatives order q inclusive and g^q in H_\beta(\Gamma).

Date received: November 8, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calu-19.