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

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3 papers · 1 filter

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.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…