A double mean field equation related to a curvature prescription problem
Analysis of PDEs
2020-02-07 v3
Abstract
We study a double mean field-type PDE related to a prescribed curvature problem on compacts surfaces with boundary. We provide a general blow-up analysis, then a Moser-Trudinger inequality, which gives energy-minimizing solutions for some range of parameters. Finally, we provide existence of min-max solutions for a wider range of parameters, which is dense in the plane if is not simply connected.
Keywords
Cite
@article{arxiv.1906.10934,
title = {A double mean field equation related to a curvature prescription problem},
author = {Luca Battaglia and Rafael López-Soriano},
journal= {arXiv preprint arXiv:1906.10934},
year = {2020}
}
Comments
29 pages, 4 figures