  We prove convergence for the nonoverlapping Robin-Robin method applied to
nonlinear elliptic equations with a $p$-structure, including degenerate
diffusion equations governed by the $p$-Laplacian. This nonoverlapping domain
decomposition is commonly encountered when discretizing elliptic equations, as
it enables the usage of parallel and distributed hardware. Convergence has been
derived in various linear contexts, but little has been proven for nonlinear
equations. Hence, we develop a new theory for nonlinear Steklov-Poincar\'e
operators based on the $p$-structure and the $L^p$-generalization of the
Lions-Magenes spaces. This framework allows the reformulation of the
Robin-Robin method into a Peaceman-Rachford splitting on the interfaces of the
subdomains, and the convergence analysis then follows by employing elements of
the abstract theory for monotone operators. The analysis is performed on
Lipschitz domains and without restrictive regularity assumptions on the
solutions.
