Exponential Dichotomies for Elliptic Equations on Multidimensional Domains
Abstract
The existence of exponential dichotomies has been well-established as a powerful tool to study existence, stability, and bifurcations of coherent structures. Currently, the application of exponential dichotomies to elliptic problems posed on multi-dimensional domains is predominately limited to the context of cylindrical spatial domains. Recent work by Beck et. al. (2021) has shown how to extend the method of spatial dynamics, in which one views a spatial variable as a time-like evolutionary variable, to general multi-dimensional spatial domains. In this paper, we show that exponential dichotomies exist for a class of spatial dynamical systems arising in this more general setting, thus allowing for their use in future analyses of coherent structures.
Keywords
Cite
@article{arxiv.2510.00917,
title = {Exponential Dichotomies for Elliptic Equations on Multidimensional Domains},
author = {Margaret Beck and Ryan Goh and Alanna Haslam-Hyde},
journal= {arXiv preprint arXiv:2510.00917},
year = {2026}
}