Abstract
We consider the solvability of a highly non-standard boundary value problem for Laplace’s equation arising when separate boundary elasticity is incorporated in the description of anti-plane deformations of a linearly elastic solid. The boundary elasticity consists of a distinct thin elastic coating bonded to part of the boundary of the solid. Interior and exterior mixed boundary problems are formulated and reduced to singular integro-differential equations from which we deduce the corresponding solvability results.
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