Vol. 9, No. 3, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 1871–2245
Issue 5, 1501–1870
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
Editors' interests
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author index
To appear
Other MSP journals
Regularity for parabolic integro-differential equations with very irregular kernels

Russell W. Schwab and Luis Silvestre

Vol. 9 (2016), No. 3, 727–772

We prove Hölder regularity for a general class of parabolic integro-differential equations, which (strictly) includes many previous results. We present a proof that avoids the use of a convex envelope as well as give a new covering argument that is better suited to the fractional order setting. Our main result involves a class of kernels that may contain a singular measure, may vanish at some points, and are not required to be symmetric. This new generality of integro-differential operators opens the door to further applications of the theory, including some regularization estimates for the Boltzmann equation.

nonlocal equations, nonsymmetric kernels, covering lemma, crawling ink spots, regularity
Mathematical Subject Classification 2010
Primary: 47G20, 35R09
Received: 3 October 2015
Accepted: 16 December 2015
Published: 17 June 2016
Russell W. Schwab
Department of Mathematics
Michigan State University
East Lansing, MI 48824
United States
Luis Silvestre
Department of Mathematics
The University of Chicago
Chicago, IL 60637
United States