Dirichlet problems for generalized Cauchy–Riemann systems with singular coefficients

Abstract

The article is devoted to the Dirichlet problem in the unit disk G for on ∂, Im w = h in z 0 = 1, where g is a given Hölder continuous function. The coefficient b belongs to a subspace of L 2(G) which is in general not contained in Lq(G), q > 2. Thus Vekua's theory is not applicable. Nevertheless we are able to prove the uniqueness of continuous solutions in .