The Brezis–Nirenberg problem for the curl–curl operator

@article{Mederski2016TheBP,
  title={The Brezis–Nirenberg problem for the curl–curl operator},
  author={Jaroslaw Mederski},
  journal={Journal of Functional Analysis},
  year={2016},
  volume={274},
  pages={1345-1380}
}
  • Jaroslaw Mederski
  • Published 2016
  • Mathematics
  • Journal of Functional Analysis
  • Abstract We look for solutions E : Ω → R 3 of the problem { ∇ × ( ∇ × E ) + λ E = | E | p − 2 E in  Ω ν × E = 0 on  ∂ Ω on a bounded Lipschitz domain Ω ⊂ R 3 , where ∇× denotes the curl operator in R 3 . The equation describes the propagation of the time-harmonic electric field ℜ { E ( x ) e i ω t } in a nonlinear isotropic material Ω with λ = − μ e ω 2 ≤ 0 , where μ and e stand for the permeability and the linear part of the permittivity of the material. The nonlinear term | E | p − 2 E with p… CONTINUE READING
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