, Volume 12, Issue 6, pp 835-854

Corner singularity for transmission problems in three dimensions

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Abstract

For a transmission problem for the Laplace operator the unique solvability is proved in natural Sobolev spaces in the case when edges and corners are present. The behaviour of the solution near the corner is reduced to the question when an explicitely given meromorphic family of one-dimensional integral operators on a geodesic polygon on the two sphere has a non-trivial kernel.