Phase separation, optimal partitions, and nodal solutions to the Yamabe equation on the sphere
Analysis of PDEs
2019-10-17 v1
Abstract
We study an optimal M-partition problem for the Yamabe equation on the round sphere, in the presence of some particular symmetries. We show that there is a correspondence between solutions to this problem and least-energy sign-changing symmetric solutions to the Yamabe equation on the sphere with precisely M nodal domains. The existence of an optimal partition is established through the study of the limit profiles of least-energy solutions to a weakly coupled competitive elliptic system on the sphere.
Keywords
Cite
@article{arxiv.1910.07101,
title = {Phase separation, optimal partitions, and nodal solutions to the Yamabe equation on the sphere},
author = {Mónica Clapp and Alberto Saldaña and Andrzej Szulkin},
journal= {arXiv preprint arXiv:1910.07101},
year = {2019}
}
Comments
16 pages and 1 figure