Magnetostatic problems in fractal domains

@article{Creo2018MagnetostaticPI,
  title={Magnetostatic problems in fractal domains},
  author={Simone Creo and Maria Rosaria Lancia and Paola Vernole and Michael Hinz and Alexander Teplyaev},
  journal={arXiv: Mathematical Physics},
  year={2018}
}
  • Simone Creo, Maria Rosaria Lancia, +2 authors Alexander Teplyaev
  • Published 2018
  • Physics, Mathematics
  • arXiv: Mathematical Physics
  • We consider a magnetostatic problem in a 3D "cylindrical" domain of Koch type. We prove existence and uniqueness results for both the fractal and pre-fractal problems and we investigate the convergence of the pre-fractal solutions to the limit fractal one. We consider the numerical approximation of the pre-fractal problems via FEM and we prove a priori error estimates. Some numerical simulations are also shown. Our long term motivation includes studying problems that appear in quantum physics… CONTINUE READING

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