6533b831fe1ef96bd1298437

RESEARCH PRODUCT

A double mean field equation related to a curvature prescription problem

Luca BattagliaRafael López-soriano

subject

Blow–up analysiPlane (geometry)Applied Mathematics010102 general mathematicsMathematics::Analysis of PDEs35J20 58J32Boundary (topology)Unit normal vectorCurvature01 natural sciencesConformal metric010101 applied mathematicsMathematics - Analysis of PDEsVariational methodsMean field equationSimply connected spaceFOS: Mathematics0101 mathematicsPrescribed curvature problemAnalysisMathematical physicsMathematicsAnalysis of PDEs (math.AP)

description

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.

yearjournalcountryeditionlanguage
2019-06-26
http://arxiv.org/abs/1906.10934