Carmelo Puliatti

activity

20172025

most cited

L^{2}

-boundedness of gradients of single layer potentials and uniform rectifiability

4 citations · 4 across the 6 of their papers we have counts for

collaborators

9 papers

math.AP2025

Layer potentials for elliptic operators with DMO-type coefficients: big pieces $T b$ theorem, quantitative rectifiability, and free boundary problems

Andrea Merlo, Mihalis Mourgoglou, Carmelo Puliatti

For $n \geq 2$ , we consider the operator $L_{A} = - div (A (\cdot) \nabla)$ , where $A$ is a uniformly elliptic $(n + 1) \times (n + 1)$ matrix with variable coefficients, a Radon mea…

math.CA2024

On Fourier transforms of fractal measures on the parabola

Tuomas Orponen, Carmelo Puliatti, Aleksi Pyörälä

Let $s \in [0, 1]$ and $t \in [0, min {3 s, s + 1})$ . Let $σ$ be a Borel measure supported on the parabola $P = {(x, x^{2}) : x \in [- 1, 1]}$ satisfying the $s$ -dimensional…

math.MG2022

On the density problem in the parabolic space

Andrea Merlo, Mihalis Mourgoglou, Carmelo Puliatti

In this work we extend many classical results concerning the relationship between densities, tangents and rectifiability to the parabolic spaces, namely $R^{n + 1}$ equipped…

math.AP2021

$L^{2}$ -boundedness of gradients of single layer potentials for elliptic operators with coefficients of Dini mean oscillation-type

Alejandro Molero, Mihalis Mourgoglou, Carmelo Puliatti +1

We consider a uniformly elliptic operator $L_{A}$ in divergence form associated with an $(n + 1) \times (n + 1)$ -matrix $A$ with real, merely bounded, and possibly non-symmetric coefficien…

math.AP2020

Blow-ups of caloric measure in time varying domains and applications to two-phase problems

Mihalis Mourgoglou, Carmelo Puliatti

We develop a method to study the structure of the common part of the boundaries of disjoint and possibly non-complementary time-varying domains in $R^{n + 1}$ , $n \geq 2$ , a…

math.AP2019

Gradient of the single layer potential and quantitative rectifiability for general Radon measures

Carmelo Puliatti

We identify a set of sufficient local conditions under which a significant portion of a Radon measure $μ$ on $R^{n + 1}$ with compact support can be covered by an $n$ -unifor…

math.CA2018★ 4 cited

$L^{2}$ -boundedness of gradients of single layer potentials and uniform rectifiability

Laura Prat, Carmelo Puliatti, Xavier Tolsa

Let $A (\cdot)$ be an $(n + 1) \times (n + 1)$ uniformly elliptic matrix with Hölder continuous real coefficients and let $E_{A} (x, y)$ be the fundamental solution of the PDE $\mat…

math.CA2018

Measures that define a compact Cauchy transform

Carmelo Puliatti

The aim of this work is to provide a geometric characterization of the positive Radon measures $μ$ with compact support on the plane such that the associated Cauchy transform defin…

math.AP2017

Estimates for the Maximal Cauchy Integral on Chord-arc Curves

Carmelo Puliatti

We study the chord-arc Jordan curves that satisfy the Cotlar-type inequality $T_{*} (f) ≲ M^{2} (T f),$ where $T$ is the Cauchy transform, $T_{*}$ is the maximal Cauchy transform and…

Layer potentials for elliptic operators with DMO-type coefficients: big pieces Tb theorem, quantitative rectifiability, and free boundary problems

On Fourier transforms of fractal measures on the parabola

On the density problem in the parabolic space

L2-boundedness of gradients of single layer potentials for elliptic operators with coefficients of Dini mean oscillation-type

Blow-ups of caloric measure in time varying domains and applications to two-phase problems

Gradient of the single layer potential and quantitative rectifiability for general Radon measures

L2-boundedness of gradients of single layer potentials and uniform rectifiability

Measures that define a compact Cauchy transform

Estimates for the Maximal Cauchy Integral on Chord-arc Curves

Layer potentials for elliptic operators with DMO-type coefficients: big pieces $T b$ theorem, quantitative rectifiability, and free boundary problems

$L^{2}$ -boundedness of gradients of single layer potentials for elliptic operators with coefficients of Dini mean oscillation-type

$L^{2}$ -boundedness of gradients of single layer potentials and uniform rectifiability