Abstract
Stationary free boundary problems related to the formation of the interface between two immiscible fluids are investigated. The corresponding models were introduced originally by Shikhmurzaev to remove singularities arising in contact-line problems. We consider two models which are derived under different assumptions for the structure of the interfacial layer, and prove the existence of rotationally symmetric solutions in Holder spaces for a sufficiently small rotationally symmetric external force.
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