2 citations · 4 across the 5 of their papers we have counts for
7 papers · 1 filter
Carleson estimates for the Green function on domains with lower dimensional boundaries
Guy David, Linhan Li, Svitlana Mayboroda
In the present paper, we consider an elliptic divergence form operator in with and prove that its Green function is almost affine, in th…
Green function estimates on complements of low-dimensional uniformly rectifiable sets
Guy David, Joseph Feneuil, Svitlana Mayboroda
It has been recently established by the first and third author that on uniformly rectifiable sets the Green function is almost affine in the weak sense, and moreover, in some scena…
Approximation of Green functions and domains with uniformly rectifiable boundaries of all dimensions
Guy David, Svitlana Mayboroda
The present paper establishes equivalence between uniform rectifiability of the boundary of a domain and the property that the Green function for elliptic operators is well approxi…
Good elliptic operators on Cantor sets
Guy David, Svitlana Mayboroda
It is well known that a purely unrectifiable set cannot support a harmonic measure which is absolutely continuous with respect to the Hausdorff measure of this set. We show that no…
Harmonic measure is absolutely continuous with respect to the Hausdorff measure on all low-dimensional uniformly rectifiable sets
G. David, S. Mayboroda
It was recently shown that the harmonic measure is absolutely continuous with respect to the Hausdorff measure on a domain with an dimensional uniformly rectifiable boundary,…
Square functions, non-tangential limits and harmonic measure in co-dimensions larger than one
Guy David, Max Engelstein, Svitlana Mayboroda
In this paper, we characterize the rectifiability (both uniform and not) of an Ahlfors regular set, E, of arbitrary co-dimension by the behavior of a regularized distance function…