J. Feneuil

activity

20142026

most citedDirichlet problem in domains with lower dimensional boundaries

10 citations · 26 across the 23 of their papers we have counts for

collaborators

27 papers

math.FA2026

Reverse inequalities for super-Riesz transforms on graphs with a slow diffusion

Joseph Feneuil

In the $D$ -dimensional Vicsek graph, we prove that the Riesz-like inequality $∥\nabla f ∥_{p} \leq C ∥ Δ^{γ} f ∥_{p}$ holds for every $p \in (1, \infty)$ and every $ 0<γ<γ^*(p):=\frac{1}{…

math.AP2026

Stability of $L^{p}$ Dirichlet problem under small bi-Lipschitz transformations of domains

Joseph Feneuil, Linhan Li, Jinping Zhuge

We show that small bi-Lipschitz deformations of a Lipschitz domain (with possibly large Lipschitz constant) preserve the solvability of the Dirichlet problem for the Laplacian with…

math.FA2025

In spaces with a slow diffusion, the Riesz transform is unbounded on $L^{p}$ , $p \in (2, \infty)$

Joseph Feneuil

In graphs and Riemannian manifolds where the kernel of the diffusion semigroup satisfies pointwise sub-Gaussian estimates, we study the range of parameters $ p \in (1, \infty) $…

math.AP2024

Carleson perturbations of locally Lipschitz elliptic operators

Joseph Feneuil

In one-sided Chord-Arc Domains $Ω$ , we demonstrate that the $A_{\infty}$ -absolute continuity of the elliptic measure with respect to the surface measure remains stable under $L^{2}$ Ca…

math.AP2024★ 1 cited

The $L^{p}$ Poisson-Neumann problem and its relation to the Neumann problem

Joseph Feneuil, Linhan Li

We introduce the $L^{p}$ Poisson-Neumann problem for an uniformly elliptic operator $L = - div A\nabla$ in divergence form in a bounded 1-sided Chord Arc Domain $Ω$ , which consider…

math.AP2023

An alternative proof of the $L^{p}$ -regularity problem for Dahlberg-Kenig-Pipher operators on $R_{+}^{n}$

Joseph Feneuil

In this article, we present a simpler and alternative proof of the solvability of the regularity problem - that is, the Dirichlet problem with boundary data in $W ˙^{1, p}$ - for…

math.AP2023

A Green function characterization of uniformly rectifiable sets of any codimension

Joseph Feneuil, Linhan Li

In this paper, we obtain a unified characterization of uniformly rectifiable sets of {\it any codimension} in terms of a Carleson estimate on the second derivatives of the Green fu…

math.AP2022

Green functions and smooth distances

Joseph Feneuil, Linhan Li, Svitlana Mayboroda

In the present paper, we show that for an optimal class of elliptic operators with non-smooth coefficients on a 1-sided Chord-Arc domain, the boundary of the domain is uniformly re…

math.AP2022

The Regularity problem in domains with lower dimensional boundaries

Zanbing Dai, Joseph Feneuil, Svitlana Mayboroda

In the present paper we establish the solvability of the Regularity boundary value problem in domains with (flat and Lipschitz) lower dimensional boundaries for operators whose coe…

math.AP2022

Carleson Perturbations for the Regularity Problem

Zanbing Dai, Joseph Feneuil, Svitlana Mayboroda

We prove that the solvability of the regularity problem in $L^{q} (\partial Ω)$ is stable under Carleson perturbations. If the perturbation is small, then the solvability is preserved…

math.AP2021

A change of variable for Dahlberg-Kenig-Pipher operators

Joseph Feneuil

In the present article, we purpose a method to deal with Dahlberg-Kenig-Pipher (DPK) operators in boundary value problems on the upper half plane. We give a nice subclass of the we…

math.AP2021★ 1 cited

Green function estimates on complements of low-dimensional uniformly rectifiable sets

Guy David, Joseph Feneuil, Svitlana Mayboroda

It has been recently established by the first and third author that on uniformly rectifiable sets the Green function is almost affine in the weak sense, and moreover, in some scena…

math.AP2020

Generalized Carleson perturbations of elliptic operators and applications

Joseph Feneuil, Bruno Poggi

We extend in two directions the notion of perturbations of Carleson type for the Dirichlet problem associated to an elliptic real second-order divergence-form (possibly degenerate,…

math.AP2020★ 2 cited

The Green function with pole at infinity applied to the study of the elliptic measure

Joseph Feneuil

In $R_{+}^{d + 1}$ or in $R^{n} ∖ R^{d}$ ( $d < n - 1$ ), we study the Green function with pole at infinity introduced by David, Engelstein, and Mayboroda. In two…

math.AP2020

Absolute continuity of the harmonic measure on low dimensional rectifiable sets

Joseph Feneuil

We consider a uniformly rectifiable set $Γ \subset R^{n}$ of dimension $d < n - 1$ . By using degenerate elliptic operators on the complement $Ω = R^{n} ∖ Γ$ , Guy Davi…

math.AP2020

Elliptic theory in domains with boundaries of mixed dimension

Guy David, Joseph Feneuil, Svitlana Mayboroda

Take an open domain $Ω \subset R^{n}$ whose boundary may be composed of pieces of different dimensions. For instance, $Ω$ can be a ball on $R^{3}$ , minus one of its diam…

math.AP2018★ 10 cited

Dirichlet problem in domains with lower dimensional boundaries

Joseph Feneuil, Svitlana Mayboroda, Zihui Zhao

The present paper pioneers the study of the Dirichlet problem with $L^{q}$ boundary data for second order operators with complex coefficients in domains with lower dimensional bounda…

math.AP2018

A new elliptic measure on lower dimensional sets

Guy David, Joseph Feneuil, Svitlana Mayboroda

The recent years have seen a beautiful breakthrough culminating in a comprehensive understanding of certain scale-invariant properties of $n - 1$ dimensional sets across analysis, ge…

math.AP2017

Dahlberg's theorem in higher co-dimension

Guy David, Joseph Feneuil, Svitlana Mayboroda

In 1977 the celebrated theorem of B. Dahlberg established that the harmonic measure is absolutely continuous with respect to the Hausdorff measure on a Lipschitz graph of dimension…

math.AP2017

Elliptic theory for sets with higher co-dimensional boundaries

Guy R. David, Joseph Feneuil, Svitlana Mayboroda

Many geometric and analytic properties of sets hinge on the properties of harmonic measure, notoriously missing for sets of higher co-dimension. The aim of this manuscript is to de…

math.AP2016

Harmonic measure on sets of codimension larger than one

Guy David, Joseph Feneuil, Svitlana Mayboroda

We introduce a new notion of a harmonic measure for a $d$ -dimensional set in $R^{n}$ with $d < n - 1$ , that is, when the codimension is strictly bigger than 1. Our measure is associated…

math.CA2015★ 2 cited

Riesz transform for $1 \leq p \leq 2$ without Gaussian heat kernel bound

Li Chen, Thierry Coulhon, Joseph Feneuil +1

We study the $L^{p}$ boundedness of Riesz transform as well as the reverse inequality on Riemannian manifolds and graphs under the volume doubling property and a sub-Gaussian heat ke…

math.PR2015★ 1 cited

About the $L^{2}$ analyticity of Markov operators on graphs

Joseph Feneuil

Let $Γ$ be a graph and $P$ be a reversible random walk on $Γ$ . From the $L^{2}$ analyticity of the Markov operator $P$ , we deduce that an iterate of odd exponent of $P$ is `lazy', th…

math.AP2015

Algebra properties for Besov spaces on unimodular Lie groups

Joseph Feneuil

We consider the Besov space $B_{α}^{p, q} (G)$ on a unimodular Lie group $G$ equipped with a sublaplacian $Δ$ . Using estimates of the heat kernel associated with $Δ$ , we give several c…

Reverse inequalities for super-Riesz transforms on graphs with a slow diffusion

Stability of Lp Dirichlet problem under small bi-Lipschitz transformations of domains

In spaces with a slow diffusion, the Riesz transform is unbounded on Lp, p∈(2,∞)

Carleson perturbations of locally Lipschitz elliptic operators

The Lp Poisson-Neumann problem and its relation to the Neumann problem

An alternative proof of the Lp-regularity problem for Dahlberg-Kenig-Pipher operators on R+n​

A Green function characterization of uniformly rectifiable sets of any codimension

Green functions and smooth distances

The Regularity problem in domains with lower dimensional boundaries

Carleson Perturbations for the Regularity Problem

A change of variable for Dahlberg-Kenig-Pipher operators

Green function estimates on complements of low-dimensional uniformly rectifiable sets

Generalized Carleson perturbations of elliptic operators and applications

The Green function with pole at infinity applied to the study of the elliptic measure

Absolute continuity of the harmonic measure on low dimensional rectifiable sets

Elliptic theory in domains with boundaries of mixed dimension

Dirichlet problem in domains with lower dimensional boundaries

A new elliptic measure on lower dimensional sets

Dahlberg's theorem in higher co-dimension

Elliptic theory for sets with higher co-dimensional boundaries

Harmonic measure on sets of codimension larger than one

Riesz transform for 1≤p≤2 without Gaussian heat kernel bound

About the L2 analyticity of Markov operators on graphs

Algebra properties for Besov spaces on unimodular Lie groups

Stability of $L^{p}$ Dirichlet problem under small bi-Lipschitz transformations of domains

In spaces with a slow diffusion, the Riesz transform is unbounded on $L^{p}$ , $p \in (2, \infty)$

The $L^{p}$ Poisson-Neumann problem and its relation to the Neumann problem

An alternative proof of the $L^{p}$ -regularity problem for Dahlberg-Kenig-Pipher operators on $R_{+}^{n}$

Riesz transform for $1 \leq p \leq 2$ without Gaussian heat kernel bound

About the $L^{2}$ analyticity of Markov operators on graphs