In this article we prove existence and uniqueness results for solutions to the outer oblique boundary problem for the Poisson equation under very weak assumptions on boundary, coefficients and inhomogeneities. Main tools are the Kelvin transformation and the solution operator for the regular inner problem, provided in [1]. Moreover we prove regularisation results for the weak solutions of both, the inner and the outer problem. We investigate the non-admissible direction for the oblique vector

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... he oblique vector field, state results with stochastic inhomogeneities and provide a Ritz-Galerkin approximation. The results are applicable to problems from Geomathematics, see e.g. [2] and [3].