Jonas Azzam

activity

20152025

most citedRectifiability of harmonic measure in domains with porous boundaries

6 citations · 6 across the 1 of their papers we have counts for

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Showing 2018Show all

4 papers · 1 filter

math.CA2018

Dimension drop for harmonic measure on Ahlfors regular boundaries

Jonas Azzam

We show that given a domain $Ω \subseteq R^{d + 1}$ with uniformly non-flat Ahlfors $s$ -regular boundary and $s \geq d$ , the dimension of its harmonic measure is strictly less…

math.CA2018

Characterization of rectifiable measures in terms of $α$ -numbers

Jonas Azzam, Xavier Tolsa, Tatiana Toro

We characterize Radon measures $μ$ in $R^{n}$ that are $d$ -rectifiable in the sense that their supports are covered up to $μ$ -measure zero by countably many $d$ -dimensiona…

math.MG2018

Accessible parts of the boundary for domains with lower content regular complements

Jonas Azzam

We show that if $0 < t < s \leq n - 1$ , $Ω \subseteq R^{n}$ with lower $s$ -content regular complement, and $z \in Ω$ , there is a chord-arc domain $Ω_{z} \subseteq Ω$ with center $z$ …

math.AP2018

Harmonic measure and quantitative connectivity: geometric characterization of the $L^{p}$ solvability of the Dirichlet problem. Part II

Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa

Let $Ω \subset R^{n + 1}$ be an open set with $n$ -AD-regular boundary. In this paper we prove that if the harmonic measure for $Ω$ satisfies the so-called weak- $A_{\infty}$ condi…

Dimension drop for harmonic measure on Ahlfors regular boundaries

Characterization of rectifiable measures in terms of α-numbers

Accessible parts of the boundary for domains with lower content regular complements

Harmonic measure and quantitative connectivity: geometric characterization of the Lp solvability of the Dirichlet problem. Part II

Characterization of rectifiable measures in terms of $α$ -numbers

Harmonic measure and quantitative connectivity: geometric characterization of the $L^{p}$ solvability of the Dirichlet problem. Part II