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Recent advances in nonlinear potential theory

  • Date November 23, 2017
  • Hour 3 pm
  • Room GSSI Main Lecture Hall
  • Speaker Giuseppe Mingione (Univ. Parma)

The classical linear potential theory deals with the fine properties of harmonic functions, and, more in general, of solutions to linear elliptic and parabolic equations. It can be therefore considered as a part of regularity theory. The analysis goes through via the use of fundamental solutions up to involving fractional and singular integrals, and the theory intersects with Harmonic Analysis. What happens when problems are genuinely nonlinear and fundamental solutions are not available? So called nonlinear potential theory comes into the play, surprisingly yielding similar but via very different means. I'll give an outline of recent progresses in this respect.