Discrete Carleman estimates and three balls inequalities
Analysis of PDEs
2021-01-27 v3
Abstract
We prove logarithmic convexity estimates and three balls inequalities for discrete magnetic Schr\"odinger operators. These quantitatively connect the discrete setting in which the unique continuation property fails and the continuum setting in which the unique continuation property is known to hold under suitable regularity assumptions. As a key auxiliary result which might be of independent interest we present a Carleman estimate for these discrete operators.
Keywords
Cite
@article{arxiv.2003.00491,
title = {Discrete Carleman estimates and three balls inequalities},
author = {Aingeru Fernández-Bertolin and Luz Roncal and Angkana Rüland and Diana Stan},
journal= {arXiv preprint arXiv:2003.00491},
year = {2021}
}
Comments
25 pages, comments welcome, relation $\tau$ and h improved, added some higher order Taylor terms in Lemma 3.3