A double mean field equation related to a curvature prescription problem
arXiv:1906.10934
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.
29 pages, 4 figures