General p-curl systems and duality mappings on Sobolev spaces for Maxwell equations

Abstract

We study a general p-curl system arising from a model of type-II superconductors. We show several trace theorems that hold on either a Lipschitz domain with small Lipschitz constant or on a C^{1,1} domain. Certain duality mappings on related Sobolev spaces are computed and used to establish surjectivity results for the p-curl system. We also solve a nonlinear boundary value problem for a general p-curl system on a C^{1,1} domain and provide a variational characterization of the first eigenvalue of the p-curl operator.
 For more information see https://ejde.math.txstate.edu/Volumes/2020/116/abstr.html