WEIGHTED ELLIPTIC ESTIMATES FOR A MIXED BOUNDARY SYSTEM RELATED TO THE DIRICHLET-NEUMANN OPERATOR ON A CORNER DOMAIN

Based on the H-2 existence of the solution, we investigate weighted estimates for a mixed boundary elliptic system in a two-dimensional corner domain, when the contact angle omega is an element of (0, pi/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 omega is an element of (0, pi).