#### Vol. 14, No. 4, 2021

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print) Author Index To Appear Other MSP Journals
Multilayer potentials for higher-order systems in rough domains

### Gustavo Hoepfner, Paulo Liboni, Dorina Mitrea, Irina Mitrea and Marius Mitrea

Vol. 14 (2021), No. 4, 1233–1308
##### Abstract

We initiate the study of multilayer potential operators associated with any given homogeneous constant-coefficient higher-order elliptic system $L$ in an open set $\Omega \subseteq {ℝ}^{n}$ satisfying additional assumptions of a geometric measure theoretic nature. We develop a Calderón–Zygmund-type theory for this brand of singular integral operators acting on Whitney arrays, starting with the case when $\Omega$ is merely of locally finite perimeter and then progressively strengthening the hypotheses by ultimately assuming that $\Omega$ is a uniformly rectifiable domain (which is the optimal setting where singular integral operators of principal value type are known to be bounded on Lebesgue spaces), and conclude by indicating how this body of results is significant in the context of boundary value problems for the higher-order system $L$ in such a domain $\Omega$.

We have not been able to recognize your IP address 100.24.118.144 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.