The existence of the solution to an elliptic system arising in electrochemical modelling is proven here. The elliptic system of interest here is composed of two diffusion equations; one of them is posed with a Dirichlet condition which couples it to the other equation on an interface, and a Signorini condition on one of the boundaries. The other one is posed with Neumann conditions, which are also coupled at an interface. The existence of the solution is proven by using Schauder's fixed point theorem, which requires some previous local regularity properties of the solution to the ``Signorini problem".
"Existence of a solution to a coupled elliptic system with a Signorini condition." Adv. Differential Equations 4 (2) 225 - 250, 1999. https://doi.org/10.57262/ade/1366291414