A concise introduction to Colombeau generalized functions and their applications in classical electrodynamics

@article{Gsponer2006ACI,
  title={A concise introduction to Colombeau generalized functions and their applications in classical electrodynamics},
  author={Andr{\'e} Gsponer},
  journal={European Journal of Physics},
  year={2006},
  volume={30},
  pages={109-126}
}
  • A. Gsponer
  • Published 26 November 2006
  • Physics, Mathematics
  • European Journal of Physics
The objective of this introduction to Colombeau algebras of generalized functions (in which distributions can be freely multiplied) is to explain in elementary terms the essential concepts necessary for their application to basic nonlinear problems in classical physics. Examples are given in hydrodynamics and electrodynamics. The problem of the self-energy of a point electric charge is worked out in detail: the Coulomb potential and field are defined as Colombeau generalized functions, and… 
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