A double mean field equation related to a curvature prescription problem

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Battaglia, Luca¹  Lopez-Soriano, Rafael² 

[1] Univ Roma Tre, Dipartimento Matemat & Fis, Largo S Leonardo Murialdo 1, I-00146 Rome, Italy

[2] Univ Valencia, Dept Anal Matemat, Dr Moliner 50, Burjassot 46100, Valencia, Spain

关键词: Prescribed curvature problem;    Conformal metric;    Variational methods;    Blow-up analysis;   

DOI  :  10.1016/j.jde.2020.02.012

来源: Elsevier

【 摘 要 】

We study a double mean field-type PDE related to a prescribed curvature problem on compacts surfaces with boundary: Here rho and rho' are real parameters, K, hare smooth positive functions on Sigma and partial derivative Sigma respectively and nu is the outward unit normal vector to partial derivative Sigma. 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 Sigma is not simply connected. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free