J. Garnett

activity

20092022

most citedUniform rectifiability from Carleson measure estimates and

ε

-approximability of bounded harmonic functions

29 citations · 53 across the 8 of their papers we have counts for

collaborators

9 papers

math.CA2022

On Extrapolation of Carleson Measures

John Garnett

We give an alternate proof of three versions of the theorem on extrapolation of Carleson measures.

math.CA2020

Carleson measure estimates and $ε$ -approximation of bounded harmonic functions, without Ahlfors regularity assumptions

John Garnett

Let $Ω$ be a domain in $R^{d + 1}$ , $d \geq 1$ . In the paper's references [HMM2] and [GMT] it was proved that if $Ω$ satisfies a corkscrew condition and if $\partial Ω$ is $…

math.CA2016★ 29 cited

Uniform rectifiability from Carleson measure estimates and $ε$ -approximability of bounded harmonic functions

John Garnett, Mihalis Mourgoglou, Xavier Tolsa

Let $Ω \subset R^{n + 1}$ , $n \geq 1$ , be a corkscrew domain with Ahlfors-David regular boundary. In this paper we prove that $\partial Ω$ is uniformly $n$ -rectifiable if every bo…

math.CA2016★ 18 cited

Uniform rectifiability, elliptic measure, square functions, and $ε$ -approximability via an ACF monotonicity formula

Jonas Azzam, John Garnett, Mihalis Mourgoglou +1

Let $Ω \subset R^{n + 1}$ , $n \geq 2$ , be an open set with Ahlfors-David regular boundary that satisfies the corkscrew condition. We consider a uniformly elliptic operator $L$ i…

math.AP2015

The regularity of the boundary of a multidimensional aggregation patch

Andrea Bertozzi, John Garnett, Thomas Laurent +1

Let $d \geq 2$ and let $N (y)$ be the fundamental solution of the Laplace equation in $R^{d}$ We consider the aggregation equation $$ \frac{\partial ρ}{\partial t} + \operatorname{div…

math.CA2014★ 2 cited

Square functions and uniform rectifiability

Vasilis Chousionis, John Garnett, Triet Le +1

In this paper it is shown that an Ahlfors-David $n$ -dimensional measure $μ$ on $R^{d}$ is uniformly $n$ -rectifiable if and only if for any ball $B (x_{0}, R)$ centered at $\oper…

math.AP2012

Image Processing Variations with Analytic Kernels

John B. Garnett, Triet M. Le, Luminita A. Vese

Let $f \in L^{1} (R^{d})$ be real. The Rudin-Osher-Fatemi model is to minimize $∥ u ∥_{B V ˙} + λ ∥ f - u ∥_{L^{2}}^{2}$ , in which one thinks of $f$ as a given image, $λ > 0$ as a "tuning para…

math.AP2012

Characterization of radially symmetric finite time blowup in multidimensional aggregation equations,

Andrea L. Bertozzi, John B. Garnett, Thomas Laurent

This paper studies the transport of a mass $μ$ in $ℜ^{d}, d \geq 2,$ by a flow field $v = - \nabla K * μ$ . We focus on kernels $K = ∣ x ∣^{α} / α$ for $2 - d \leq α < 2$ for which the smooth den…

math.MG2009★ 4 cited

A doubling measure on $R^{d}$ can charge a rectifiable curve

John Garnett, Rowan Killip, Raanan Schul

For $d \geq 2$ , we construct a doubling measure $ν$ on $R^{d}$ and a rectifiable curve $Γ$ such that $ν (Γ) > 0$ .