Vol. 9, No. 2, 2016

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

Volume 16
Issue 7, 1485–1744
Issue 6, 1289–1483
Issue 5, 1089–1288
Issue 4, 891–1088
Issue 3, 613–890
Issue 2, 309–612
Issue 1, 1–308

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
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
A counterexample to the Hopf–Oleinik lemma (elliptic case)

Darya E. Apushkinskaya and Alexander I. Nazarov

Vol. 9 (2016), No. 2, 439–458
Abstract

We construct a new counterexample to the Hopf–Oleinik boundary point lemma. It shows that for convex domains, the C1,Dini assumption on Ω is the necessary and sufficient condition providing the estimates of Hopf–Oleinik type.

Dedicated to Professor M.V. Safonov

Keywords
elliptic equations, Hopf–Oleinik lemma, Dini continuity, counterexample
Mathematical Subject Classification 2010
Primary: 35J15, 35B45
Milestones
Received: 2 April 2015
Revised: 29 September 2015
Accepted: 16 December 2015
Published: 24 March 2016
Authors
Darya E. Apushkinskaya
Department of Mathematics
Saarland University
P.O. Box 151150
Saarbrücken 66041
Germany
St. Petersburg State University
7/9 Universitetskaya nab.
St. Petersburg 199034
Russia
Alexander I. Nazarov
St. Petersburg Department
Steklov Institute
Fontanka 27
St. Petersburg 191023
Russia
St. Petersburg State University
7/9 Universitetskaya nab.
St. Petersburg 199034
Russia