Mihalis Mourgoglou

activity

20102026

most citedRectifiability of harmonic measure

61 citations · 237 across the 33 of their papers we have counts for

collaborators

Showing 2018Show all

2 papers · 1 filter

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…

math.CA2018

Failure of $L^{2}$ boundedness of gradients of single layer potentials for measures with zero low density

José M. Conde-Alonso, Mihalis Mourgoglou, Xavier Tolsa

Consider a totally irregular measure $μ$ in $R^{n + 1}$ , that is, the upper density $lim sup_{r \to 0} \frac{μ ( B ( x , r ))}{( 2 r ) ^{n}}$ is positive $μ$ -a.e.\ in $R^{n + 1}$ , an…

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

Failure of L2 boundedness of gradients of single layer potentials for measures with zero low density

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

Failure of $L^{2}$ boundedness of gradients of single layer potentials for measures with zero low density