On a generalized Riemann-Hilbert boundary value problem for second order elliptic systems in the plane

As a consequence of the unique solvability of the modified Dirichlet problem in a multiply-connected domain it is possible to represent analytic functions in form of Cauchy type integrals with real density satisfying a Holder condition on the boundary [9]. Such a representation is used in the present paper to investigate the problem partial derivative (2)w/partial derivative (z) over bar (2) + q(z) partial derivative (2)w/partial derivative z partial derivative (z) over bar + a(z) partial derivative w/partial derivative (z) over bar + b(z) partial derivative w/partial derivative z + c(z)w = f(z) in D a(k)(t) partial derivative u/partial derivative x(2-k)partial derivative y(k-1) + b(k)(t) partial derivative v/partial derivative x(2-k)partial derivative y(k-1) = c(k)(t), k = 1,2 on gamma where w = u + iv is an element of W-p(2) (D) over bar, 2 < p and gamma equivalent to partial derivative D. The theory of two-dimensional singular integral equations [7] is applied here. In [1, 2] other Riemann-Hilbert problems for second and higher order elliptic systems in the plane are investigated.