Elliptic estimates for the Dirichlet-Neumann operator on a corner domain

We consider the elliptic estimates for the Dirichlet-Neumann operator related to the water waves problem on a two-dimensional corner domain in this paper. Due to the singularity of the boundary, there will be singular parts in the solution of the elliptic problem for the D-N operator. To begin with, we study elliptic problems with mixed boundary conditions to derive singularity decompositions and estimates. Based on this analysis, we present the estimates for both the D-N operator and its shape derivative with the existence of singular parts.NSFC [11401598]SCI(E)ARTICLE3-4103-16610