Quantitative unique continuation for Robin boundary value problems on $C^{1,1}$ domains
Abstract
In this paper, we prove two unique continuation results for second order elliptic equations with Robin boundary conditions on domains. The first one is a sharp vanishing order estimate of Robin problems with Lipschitz coefficients and differentiable, sign-changing potentials. This generalizes the result for the "Robin eigenfunctions" in [26], which deals with the case with constant potentials. The second result is a unique continuation result from the boundary -- any non-trivial solution cannot vanish at infinite order from the boundary or vanish on an open subset on the boundary. Such result generalizes the one in [1] for the Laplace equation on domains with zero Neumann boundary conditions.
Keywords
Cite
@article{arxiv.2111.01766,
title = {Quantitative unique continuation for Robin boundary value problems on $C^{1,1}$ domains},
author = {Zongyuan Li and Weinan Wang},
journal= {arXiv preprint arXiv:2111.01766},
year = {2022}
}
Comments
Updated some references, corrected typos and minor mistakes, and reorganized some parts in Sections 2 and 3