Weighted elliptic estimates for a mixed boundary system related to the Dirichlet-Neumann operator on a corner domain

Abstract

Based on the H2 existence of the solution, we investigate weighted estimates for a mixed boundary elliptic system in a two-dimensional corner domain, when the contact angle ω ∈ (0, π/2). This system is closely related to the Dirichlet-Neumann operator in the water-waves problem, and the weight we choose is decided by singularities of the mixed boundary system. Meanwhile, we also prove similar weighted estimates with a different weight for the Dirichlet boundary problem as well as the Neumann boundary problem when ω ∈ (0, π).