ABSTRACT
This chapter presents the context of a generalized 2-layer free-boundary problem, of which the 2-layer fluid problem is the best known special case. In the 2-layer fluid problem, one seeks an interface between the fluid layers (the free boundary) such that the derivatives of the stream functions in the layers satisfy a joining condition across the interface which corresponds to Bernoulli’s law. In the generalized problem (in arbitrary space dimensions), the derivatives of several distinct capacitary potentials defined in the first layer are required to be related to the derivatives of several distinct capacitary potentials defined in the second layer by means of a given, nonlinear joining condition across the unknown layer-interface. The chapter aims to generalize the operator method to the case of general nonlinear joining conditions, since all previous applications have been restricted to the specific form motivated by Bernoulli’s law.
