Absolutely minimizing Lipschitz extension with discontinuous boundary data

Abstract Aronsson's notion of absolutely minimizing Lipschitz extension, solution of the nonlinear equation D2u(Du, Du) = 0 in the viscosity sense, well defined in a bounded domain with continuous boundary condition, is extended to the case of a boundary condition having a finite number of jumps. This extension with discontinuous boundary data is relevant in image interpolation theory.