Solvability in the Large and Boundary Value Problems for Mizohata Type Operators

In this paper we seek for (Hölder) continuous global solutions to the equation Lu=f in the plane, for f belonging to a subspace of L^p(ℝ^2) , p≥ 1 , where L is a degenerate elliptic vector field of Mizohata type. Our approach is via the study of an associated integral operator. Also, we obtain bounded Hölder continuous solutions to Vekua type equations in the form Lu=au+bu+f . As an application we study an associated Riemann boundary value problem.