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arXiv:1512.03271 [math.AP]AbstractReferencesReviewsResources

Elliptic estimates for Dirichlet-Neumann operator on a corner domain

Mei Ming, Chao Wang

Published 2015-12-10Version 1

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.

Comments: 54 pages, 1 figures
Categories: math.AP
Subjects: 35Q35
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