Mean field equations and domains of first kind
Analysis of PDEs
2020-01-07 v1
Abstract
In this paper we are interested in understanding the structure of domains of first and second kind, a concept motivated by problems in statistical mechanics. We prove some openness property for domains of first kind with respect to a suitable topology, as well as some sufficient condition for a simply connected domain to be of first kind in terms of the Fourier coefficients of the Riemann map. Finally, we show that the set of simply connected domains of first kind is contractible.
Keywords
Cite
@article{arxiv.2001.01654,
title = {Mean field equations and domains of first kind},
author = {Daniele Bartolucci and Andrea Malchiodi},
journal= {arXiv preprint arXiv:2001.01654},
year = {2020}
}
Comments
15 pages