Heat kernel estimates for boundary trace of reflected diffusions on uniform domains

N Kajino, M Murugan - arXiv preprint arXiv:2312.08546, 2023 - arxiv.org
We study boundary trace process of a reflected diffusion for uniform domains. We obtain
stable-like heat kernel estimates for the boundary trace process of a reflected diffusion for …

Small 𝐴_ {∞} results for Dahlberg-Kenig-Pipher operators in sets with uniformly rectifiable boundaries

G David, L Li, S Mayboroda - Transactions of the American Mathematical …, 2023 - ams.org
In the present paper we consider elliptic operators $ L=-div (A\nabla) $ in a domain bounded
by a chord-arc surface $\Gamma $ with small enough constant, and whose coefficients $ A …

Optimal Poisson kernel regularity for elliptic operators with Hölder continuous coefficients in vanishing chord-arc domains

S Bortz, T Toro, Z Zhao - Journal of Functional Analysis, 2023 - Elsevier
We show that if Ω is a vanishing chord-arc domain and L is a divergence-form elliptic
operator with Hölder-continuous coefficient matrix, then log⁡ k L∈ VMO, where k L is the …

An alternative proof of the -regularity problem for Dahlberg-Kenig-Pipher operators on

J Feneuil - arXiv preprint arXiv:2310.00645, 2023 - arxiv.org
In this article, we give an alternative and simpler proof of the solvability of the regularity
problem-ie the Dirichlet problem with boundary data in $ W^{1, p} $-for uniformly elliptic …

[PDF][PDF] A theorem of Fefferman, Kenig and Pipher re-revisited

S Bortz, M Egert, O Saari - Preprint, 2021 - researchgate.net
Here we investigate the small constant case of a characterization of A∞ weights due to
Fefferman, Kenig and Pipher. We also give an application of our result to the study of elliptic …

Carleson Conditions for Weights: The quantitative small constant case

S Bortz, M Egert, O Saari - arXiv preprint arXiv:2107.14217, 2021 - arxiv.org
We investigate the small constant case of a characterization of $ A_\infty $ weights due to
Fefferman, Kenig and Pipher. In their work, Fefferman, Kenig and Pipher bound the …