00:00:00 / 00:00:00

Harmonic measure with Robin boundary conditions

By Guy David

Appears in collection : Analysis on fractals and networks, and applications / Analyse sur les fractals et les réseaux, et applications

Joint work with Stefano Decio, Max Engelstein, Mario Michetti, and Svitlana Mayboroda. The Robin boundary condition is $\frac{1}{a} \frac{\partial u}{\partial n}+u=f$ on the boundary of a domain $U$, and we claim that for $0< a< +\infty$, the corresponding harmonic measure is mutually absolutely continuous with respect to surface measure. Here (we hope we will have finished checking that) we can consider any bounded domain $U$ in $\mathbb{R}^n$ whose boundary is Ahlfors regular of dimension $d$, $n-2< d< n$, with nontangential access. The Robin condition is then to be taken weakly, and surface measure becomes Hausdorff measure.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.20151603
  • Cite this video David, Guy (19/03/2024). Harmonic measure with Robin boundary conditions. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20151603
  • URL https://dx.doi.org/10.24350/CIRM.V.20151603


Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow


  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
  • Get notification updates
    for your favorite subjects
Give feedback