Optimal three-ball inequalities and quantitative uniqueness for the Stokes system
Analysis of PDEs
2008-12-22 v1
Abstract
In this paper we study the local behavior of a solution to the Stokes system with singular coefficients. One of the main results is the bound on the vanishing order of a nontrivial solution to the Stokes system, which is a quantitative version of the strong unique continuation property. Our proof relies on some delicate Carleman-type estimates. We first use these estimates to derive crucial \emph{optimal} three-ball inequalities. Taking advantage of the optimality, we then derive an upper bound on the vanishing order of any nontrivial solution to the Stokes system from those three-ball inequalities.
Keywords
Cite
@article{arxiv.0812.3730,
title = {Optimal three-ball inequalities and quantitative uniqueness for the Stokes system},
author = {Ching-Lung Lin and Jenn-Nan Wang},
journal= {arXiv preprint arXiv:0812.3730},
year = {2008}
}