Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 116, pp. 1-22.

Title: General p-curl systems and duality mappings on Sobolev spaces for Maxwell equations
       
Authors: Dhruba R. Adhikari (Kennesaw State Univ., Kennesaw, GA, USA)
         Eric Stachura      (Kennesaw State Univ., Kennesaw, GA, USA)

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. 
 
Submitted January 19, 2020. Published November 24, 2020.
Math Subject Classifications: 49J40, 46E35, 49J50.
Key Words: p-curl operator; duality mappings; trace theorems; Nemytskii operator.