The variable exponent compound boundary value problem for Liapunov open curve

Abstract

In this paper, we study the compound boundary value problem for a class of Cauchy-type integrals with density in variable exponent space. Based on the Smirnov theorem for multi-connected domains and the elimination method, we transform the compound boundary value problem of open curve into that of closed curve. The solvable condition and the explicit solution are obtained by the elimination method.