DOI 10.1007/s10958-018-3879-9 Journal of Mathematical Sciences, Vol. 232, No. 4, July, 2018 A COUNTEREXAMPLE RELATED TO THE REGULARITY OF THE p-STOKES PROBLEM M. Kˇrepela Institute of Applied Mathematics, University of Freiburg Eckerstr. 1, D-79104 Freiburg, Germany firstname.lastname@example.org M. R˚ uˇziˇcka Institute of Applied Mathematics, University of Freiburg Eckerstr. 1, D-79104 Freiburg, Germany email@example.com UDC 517.9 1,s 2,q We construct a solenoidal vector ﬁeld u belonging to W (Ω) ∩ W (Ω), q ∈ (1,n), s ∈ p−2 (1, ∞), such that (1 + |Du|) , p ∈ (1, ∞), p =2, does not belong to the Muckenhoupt class A (Ω). Thus, one cannot use the Korn inequality in weighted Lebesgue spaces to prove the natural regularity of the p-Stokes problem. Bibliography:28 titles. Dedicated to V. V. Zhikov 1 Introduction The question of full natural regularity for the p-Stokes system − div S(Du)+ ∇π = f in Ω, (1.1) div u =0 in Ω, is still not completely solved in the three- and higher-dimensional situation. Here, Ω ⊂ R , n 2, is a bounded domain. The unknowns are the velocity vector ﬁeld u =(u ,...,u ) and 1 n the scalar pressure π, while the external body force
Journal of Mathematical Sciences – Springer Journals
Published: Jun 5, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera