On the riemann boundary value problem for holomorphic functions in the sobolev space W_1,p(D)

Abstract

This paper considers the problem of linear conjugation

on a closed Ljapunov curve , which encloses the finite domain D′. It is assumed that the coefficient on γ. The free term g belongs to the Slobodeckii space .

It is shown that the solution , 1≤p≤ x, exists and it is given explicitly, for both cases that Index G≥0 and Index G<0. In both cases an a priori estimate of the solution is given.

AMS No.:

• 30D35