Stability estimates for discrete harmonic functions on product domains
Analysis of PDEs
2016-11-26 v1
Abstract
We study the Dirichlet problem for discrete harmonic functions in unbounded product domains on multidimensional lattices. First we prove some versions of the Phragm\'en-Lindel\"of theorem and use Fourier series to obtain a discrete analog of the three-line theorem for the gradients of harmonic functions in a strip. Then we derive estimates for the discrete harmonic measure and use elementary spectral inequalities to obtain stability estimates for Dirichlet problem in cylinder domains.
Cite
@article{arxiv.1306.1997,
title = {Stability estimates for discrete harmonic functions on product domains},
author = {Maru Guadie},
journal= {arXiv preprint arXiv:1306.1997},
year = {2016}
}