Author:
Adhikari Dhruba R.,Stachura Eric
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
Reference33 articles.
1. R. A. Adams, John J. F. Fournier; Sobolev Spaces, vol. 140, Elsevier, 2003.
2. D. R. Adhikari; Nontrivial solutions of inclusions involving perturbed maximal monotone operators, Electron. J. Differential Equations 2017 (2017), no. 151, 1-21.
3. C. Amrouche, N. H. Seloula; Lp-theory for vector potentials and Sobolev's inequalities for vector fields: Application to the Stokes equations with pressure boundary condition, Mathematical Models and Methods in Applied Sciences 23 (2013), no. 01, 37-92. https://doi.org/10.1142/S0218202512500455
4. A. Anane. J. P. Gossez; Strongly nonlinear elliptic problems near resonance: a variational approach, Communications in Partial Differential Equations 15 (1990), no. 8, 1141-1159. https://doi.org/10.1080/03605309908820717
5. V. Barbu; Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff Int. Publ., Leyden (The Netherlands), 1975. https://doi.org/10.1007/978-94-010-1537-0