2018/10/30 by Joseph Esposito, Esposito, Joseph
Mathematics · Physics and Astronomy · #35J20 #46E35 #46N50 #81V70 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:35J20 #msc:46E35 #msc:46N50 #msc:81V70
paper · pdf · doi:10.48550/arxiv.1810.12991
arxiv created 2018/10/30 · arxiv updated 2018/11/01
In this paper, we utilize weighted Sobolev spaces to establish an existence theory for infinite energy solutions to a coupled non-linear elliptic system. This system describes the fractional quantum Hall effect in two-dimensional double-layered systems. Via variational methods in a suitable weighted Sobolev space, we prove the existence of multiple vortices over the full plane. These methods include constrained minimization of an action functional and the existence of a critical point, known as a saddle point, by way of a mountain pass theorem. Furthermore, for these solutions, which are necessarily of infinite energy, we establish exponential decay estimates.