2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141050We calculate explicitly solutions to the Dirichlet and Neumann boundary value problems in the upper half plane, for a family of divergence form equations with non symmetric coefficients with a jump discontinuity. It is shown that the boundary equation method and the Lax--Milgram method for constructing solutions may give two different solutions when the coefficients are sufficiently non symmetric.Revised version. To appear in Transactions of the American Mathematical SocietyAnalysis of PDEsClassical Analysis and ODEs35J25, 42A50text