A double mean field equation related to a curvature prescription problem

2019/06/26 by Battaglia, Luca, López-Soriano, Rafael
#35J20 #58J32 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/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.

Related

• A mean field problem approach for the double curvature prescription problem
• The Dirichlet problem for a prescribed mean curvature equation
• A Harnack-Type Inequality for a Prescribing Curvature equation on a Domain with Boundary
• A blow-up method to prescribed mean curvature graphs with fixed boundaries
• A Trudinger-Moser inequality on compact Riemannian surface involving Gaussian curvature