Electron. J. Differential Equations, Vol. 2020 (2020), No. 116, pp. 1-22.

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

Dhruba R. Adhikari, Eric Stachura

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.
DOI: 10.58997/ejde.2020.116

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Dhruba R. Adhikari
Department of Mathematics
Kennesaw State University
Kennesaw, Georgia 30060, USA
email: dadhikar@kennesaw.edu
Eric Stachura
Department of Mathematics
Kennesaw State University
Kennesaw, Georgia 30060, USA
email: eric.stachura@kennesaw.edu

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