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On Friedrichs-type inequalities in domains rarely perforated along the boundary
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0001-8211-3671
2011 (English)In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2011Article in journal (Refereed) Published
Abstract [en]

This paper is devoted to the Friedrichs inequality, where the domain isperiodically perforated along the boundary. It is assumed that the functionssatisfy homogeneous Neumann boundary conditions on the outer boundary andthat they vanish on the perforation. In particular, it is proved that thebest constant in the inequality converges to the best constant in aFriedrichs-type inequality as the size of the perforation goes to zero muchfaster than the period of perforation. The limit Friedrichs-type inequalityis valid for functions in the Sobolev space $H^{1}$.

Place, publisher, year, edition, pages
2011. Vol. 2011
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-7684DOI: 10.1186/1029-242X-2011-129Local ID: 616f9d49-e360-4b64-a56c-3dc84e44a552OAI: oai:DiVA.org:ltu-7684DiVA: diva2:980574
Note
Validerad; 2011; Bibliografisk uppgift: Article no 129 ; 20111206 (wall)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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