The hyperbolic dirichlet problem

The aim of this paper is to take into account the hyperbolic Dirichlet problem on a given transitive curve of the plane. Owing to a representation theorem, we can assume without loss of generality, that our curve is an ellipse. Therefore, given an ellipse and a smooth function on its boundary, we show that there are uncountably many rotations which assure existence and unicity for the corresponding solution of the hyperbolic Dirichlet problem. Moreover, we give a numerical algorithm for the effective computation of the solution.