DOI 10.1007/s10958-018-3873-2 Journal of Mathematical Sciences, Vol. 232, No. 3, July, 2018 THE NORM RESOLVENT CONVERGENCE FOR ELLIPTIC OPERATORS IN MULTI-DIMENSIONAL DOMAINS WITH SMALL HOLES D. I. Borisov Institute of Mathematics, USC RAS 112, Chernyshevskii St., Ufa 450008, Russia Bashkir State Pedagogical University 3a, October Revolution St., Ufa 450000, Russia University of Hradec Kr´ alov´e 62, Rokitansk´eho, Hradec Kr´ alov´e 50003, Czech Republic firstname.lastname@example.org A. I. Mukhametrakhimova Bashkir State Pedagogical University 3a, October Revolution St., Ufa 450000, Russia email@example.com UDC 517.956+517.958 We consider a second order elliptic operator with variable coeﬃcients in a multi- dimensional domain with a small hole and some classical boundary condition on the hole boundary. We show that the resolvent of this operator converges to the resolvent of the limit operator in the domain without holes in the sense of the norm of bounded operators acting from L to W . For the convergence rate we obtain sharp estimates relative to the smallness order. Bibliography:28 titles. Dedicated to the memory of Vasilii Vasil’evich Zhikov Boundary value problems in domains with small holes are related to the classical theory of singular perturbations. A small hole is one of the simplest examples of a geometric perturbation to
Journal of Mathematical Sciences – Springer Journals
Published: Jun 2, 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