Elliptic estimates for Dirichlet-Neumann operator on a corner domain

Abstract

We consider the elliptic estimates for Dirichlet-Neumann operator related to the water-wave 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 D-N operator. To begin with, we study elliptic problems with mixed boundary condition to derive singularity decompositions and estimates. Based on the analysis, we present the estimates for both D-N operator and its shape derivative with the existence of singular parts.

54 pages, 1 figures

References in corpus (3)

• A blow-up criteria and the existence of 2d gravity water waves with angled crests
• A Priori Estimates for Two-Dimensional Water Waves with Angled Crests
• Wellposedness and singularities of the water wave equations