J. Feneuil

activity

20242026

collaborators

6 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 $∥\nabla f ∥_{p} \leq C ∥ I^^{3} f ∥_{p}$ holds for every $p \in (1, \infty)$ and every $ 0<Î³<Î³^*(p):=\frac…

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.AP2025

Carleson perturbations of locally Lipschitz elliptic operators

Joseph Feneuil

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

math.AP2025

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.AP2024

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 $I^c ◯$ , which conside…

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

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

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

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 $L^{p}$ , $p \in (2, \infty)$

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

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