PDEA Seminar: Solvability of the Lp Dirichlet problem for the heat equation and parabolic uniform rectifiability

  • Date: –11:15
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 Å64119 + Zoom
  • Lecturer: Kaj Nyström
  • Organiser: Matematiska institutionen
  • Contact person: Kaj Nyström
  • Seminarium

Welcome to this seminar held by Kaj Nyström with the title "Solvability of the Lp Dirichlet problem for the heat equation and parabolic uniform rectifiability".

Participate on site or via Zoom link, meeting ID: 67226102216

Abstract: In recent works we solve two conjectures concerning the Lp Dirichlet problem for the heat equation, caloric measure, and parabolic uniform rectifiability. In [BHMN1] we prove that solvability of the Lp Dirichlet problem is equivalent to parabolic uniform rectifiability in the case of a parabolic Lipschitz graph. In [BHMN2] we prove, in the context of parabolic Ahlfors-David regular boundaries, that solvability of the Lp Dirichlet problem implies parabolic uniform rectifiability. The purpose of the talk is to briefly discuss these results.

[BHMN1]: Simon Bortz, Steve Hofmann, Jose Maria Martell, and Kaj Nyström. Solvability of the Lp Dirichlet problem for the heat equation is equivalent to parabolic uniform rectifiability in the case of a parabolic Lipschitz graph, manuscript, 2023.

[BHMN2]: Simon Bortz, Steve Hofmann, Jose Maria Martell, and Kaj Nyström. Solvability of the Lp Dirichlet problem for the heat equation implies parabolic uniform rectifiability, manuscript, 2023.

This is a seminar in the PDEs and Applications seminar series.

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