Abstract
AbstractIn this paper we discuss elliptic transmission problems of second order in plane non‐smooth domains with non‐homogeneous boundary data. It is known that if the boundary data are homogeneous, then the variational solution of the transmission problem admits a representation as a sum of a regular function and certain singular functions, analogous to that encountered in boundary value problems on corner domains. We determine for which domains arbitrary non‐homogeneous boundary data can be reduced to the homogeneous ones preserving availability of the representation formula. In the remaining cases we find the compatibility conditions for the data which also yield such a reduction.
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