Download this article
 Download this article For screen
For printing
Recent Issues
Volume 12, Issue 1
Volume 11, Issue 4
Volume 11, Issue 3
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 4
Volume 10, Issue 3
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 3-4
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 3-4
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN (electronic): 2325-3444
ISSN (print): 2326-7186
Author index
To appear
Other MSP journals
This article is available for purchase or by subscription. See below.
Fractional Korn's inequalities without boundary conditions

Davit Harutyunyan, Tadele Mengesha, Hayk Mikayelyan and James M. Scott

Vol. 11 (2023), No. 4, 497–524

Motivated by a linear nonlocal model of elasticity, this work establishes fractional analogues of Korn’s first and second inequalities for vector fields in fractional Sobolev spaces defined over a bounded domain. The validity of the inequalities require no additional boundary condition, extending existing fractional Korn’s inequalities that are only applicable for Sobolev vector fields satisfying zero Dirichlet boundary conditions. The domain of definition is required to have a C1-boundary or, more generally, a Lipschitz boundary with small Lipschitz constant. We conjecture that the inequalities remain valid for vector fields defined over any Lipschitz domain. We support this claim by presenting a proof of the inequalities for vector fields defined over planar convex domains.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription only.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at
or by using our contact form.

fractional Korn inequality, fractional Hardy inequality, peridynamics
Mathematical Subject Classification
Primary: 45F99, 74B99, 74G65
Received: 28 February 2023
Revised: 5 September 2023
Accepted: 3 October 2023
Published: 1 December 2023

Communicated by Micol Amar
Davit Harutyunyan
Department of Mathematics
University of California Santa Barbara
Santa Barbara, CA
United States
Tadele Mengesha
Department of Mathematics
University of Tennessee Knoxville
Knoxville, TN
United States
Hayk Mikayelyan
School of Mathematical Sciences
University of Nottingham Ningbo
James M. Scott
Department of Applied Physics and Applied Mathematics
Columbia University
New York, NY
United States