An alternative proof of the solvability of the $$L^p$$-regularity problem for Dahlberg-Kenig-Pipher operators on $${\mathbb {R}}^n_+$$
Year: 2025
Type: article
Abstract: 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 $$\dot{W}^{1,p}$$ W ˙ 1 , p —for uniformly elliptic operators on $${\mathbb {R}}^n_+$$ R + n under a (possibly large) Carleson measure condition. In addition, we slightly expand the class of operators for which the regularity problem is solvable, and establish an analogous result for weighted uniformly elliptic operators on $${\mathbb {R}}^n \setminus {\mathbb {R}}^d$$ R n \ R d , where $$d < n - 1$$ d < n - 1 .
Source: Mathematische Zeitschrift
Author: Joseph Feneuil
Institutions: Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Funder: Université Paris-Saclay
OpenAlex ID: W4413835624