Global Holder regularity for discontinuous elliptic equations in the plane

C-1,C-mu-regularity up to the boundary is proved for solutions of boundary value problems for elliptic equations with discontinuous coefficients in the plane. In particular, we deal with the Dirichlet boundary condition u = g(x) on partial derivativeOmega where g(x) is an element of W-2-1/r,W-r (partial derivativeOmega), r > 2, or with the following normal derivative boundary conditions: partial derivativeu/partial derivativen = h(x) or partial derivativeu/partial derivativen + sigmau = h(x) on partial derivativeOmega where h(x) is an element of W-1-1/r,W-r (partial derivative Omega), r > 2, sigma > 0 and n is the unit outward normal to the boundary partial derivativeOmega.