Quantitative uniqueness for elliptic equations at the boundary of $C^{1, Dini}$ domains
Analysis of PDEs
2016-05-10 v1
Abstract
Based on a variant of the frequency function approach of Almgren, we establish an optimal upper bound on the vanishing order of solutions to variable coefficient Schr\"odinger equations at a portion of the boundary of a domain. Such bound provides a quantitative form of strong unique continuation at the boundary. It can be thought of as a boundary analogue of an interior result recently obtained by Bakri and Zhu for the standard Laplacian.
Keywords
Cite
@article{arxiv.1605.02363,
title = {Quantitative uniqueness for elliptic equations at the boundary of $C^{1, Dini}$ domains},
author = {Agnid Banerjee and Nicola Garofalo},
journal= {arXiv preprint arXiv:1605.02363},
year = {2016}
}