141 citations · 790 across the 75 of their papers we have counts for
8 papers · 1 filter
Non-local distance functions and geometric regularity
Max Engelstein, Cole Jeznach, Svitlana Mayboroda
We establish the equivalence between the regularity (rectifiability) of sets and suitable estimates on the oscillation of the gradient for smooth non-local distance functions. A pr…
Harmonic measure is rectifiable if it is absolutely continuous with respect to the co-dimension one Hausdorff measure
Jonas Azzam, Steve Hofmann, José María Martell +4
In the present paper we sketch the proof of the fact that for any open connected set , , and any with $0<\mathcal{H}^n(E)<\…
Rectifiability of harmonic measure
Jonas Azzam, Steve Hofmann, José María Martell +4
In the present paper we prove that for any open connected set , , and any with , absolute continui…
Maximal Function Characterizations of Hardy Spaces Associated to Homogeneous Higher Order Elliptic Operators
Jun Cao, Svitlana Mayboroda, Dachun Yang
Let be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients and be the maximal interval of exponents $…
A free boundary problem for the localization of eigenfunctions
Guy David, Marcel Filoche, David Jerison +1
We study a variant of the Alt, Caffarelli, and Friedman free boundary problem with many phases and a slightly different volume term, which we originally designed to guess the local…
Uniform Rectifiability and Harmonic Measure III: Riesz transform bounds imply uniform rectifiability of boundaries of 1-sided NTA domains
Steve Hofmann, José María Martell, Svitlana Mayboroda
Let , , be a closed, Ahlfors-David regular set of dimension satisfying the "Riesz Transform bound" $$\sup_{\varepsilon>0}\int_E\left|\int_{\{…