Harmonic measure and quantitative connectivity: geometric characterization of the $$L^p$$-solvability of the Dirichlet problem
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DOI: 10.1007/s00222-020-00984-5
Abstract: Let $\Omega\subset\mathbb R^{n+1}$ be an open set with $n$-AD-regular boundary. In this paper we prove that if the harmonic measure for $\Omega$ satisfies the so-called weak-$A_\infty$ condition, then $\Omega$ satisfies a suitable connectivity condition, namely… read more here.
Keywords: dirichlet problem; geometric characterization; connectivity; condition ... See more keywords
Scaling limits of anisotropic growth on logarithmic time-scales
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DOI: 10.1214/23-ejp964
Abstract: We study the anisotropic version of the Hastings-Levitov model AHL$(\nu)$. Previous results have shown that on bounded time-scales the harmonic measure on the boundary of the cluster converges, in the small-particle limit, to the solution… read more here.
Keywords: time; logarithmic time; time scales; harmonic measure ... See more keywords
On a Property of Harmonic Measure on Simply Connected Domains
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DOI: 10.4153/s0008414x19000592
Abstract: Abstract Let $D\subset \mathbb{C}$ be a domain with $0\in D$. For $R>0$, let $\widehat{\unicode[STIX]{x1D714}}_{D}(R)$ denote the harmonic measure of $D\cap \{|z|=R\}$ at $0$ with respect to the domain $D\cap \{|z|0$. Thus, the arising question, first… read more here.
Keywords: widehat unicode; unicode stix; stix x1d714; harmonic measure ... See more keywords