RESUMEN

This paper describes the solvability of Dirichlet problems for Laplace’s equation when the boundary data is not smooth enough for the existente of a weak solution in H¹ (Ω). Scales of spaces of harmonic functions and boundary traces are defined and the solutions are characterized as limits of classical harmonic functions in special norms. The generalizad harmonic functions, and their norms, are defined using series expansions involving harmonic Steklov eigenfuctions on the domain. It is known that the usual trace operator has continuous extention to an isometirc isomorphism of specific spaces. This provides a chracterization of the generalized solutions of harmonic Dirichlet problems. Numerical simulations of a model problem are descibed. This problem is related to dewetting of thin films and the sociated phenomenology is described.