Uniform bounds for solutions to elliptic problems on simply connected planar domains
Analysis of PDEs
2018-12-11 v2
Abstract
We consider the singular Liouville equation and the Henon-Lane-Emden problem on simply connected planar domains. We show that any solution to each problem must satisfy a uniform bound on the mass. The same results applies to some systems and more general non-linearities. The proofs are based on the Riemann mapping theorem and a Pohozaev-type identity.
Keywords
Cite
@article{arxiv.1809.05684,
title = {Uniform bounds for solutions to elliptic problems on simply connected planar domains},
author = {Luca Battaglia},
journal= {arXiv preprint arXiv:1809.05684},
year = {2018}
}
Comments
9 pages, accepted on Proceedings of the American Mathematical Society