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- Chechkin, Gregory, et al.
(författare)
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A new weighted Friedrichs-type inequality for a perforated domain with a sharp constant
- 2011
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Ingår i: Eurasian Mathematical Journal. - 2077-9879. ; 2:1, s. 81-103
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Tidskriftsartikel (refereegranskat)abstract
- We derive a new three-dimensional Hardy-type inequality for a cube for the class of functions from the Sobolev space $H^1$ having zero trace on small holes distributed periodically along the boundary. The proof is based on a careful analysis of the asymptotic expansion of the first eigenvalue of a related spectral problem and the best constant of the corresponding Friedrichs-type inequality.
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| 5. |
- Chechkin, Gregory, et al.
(författare)
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On spectrum of the Laplacian in a circle perforated along the boundary : Application to a Friedrichs-type inequality
- 2011
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Ingår i: International Journal of Differential Equations. - : Hindawi Limited. - 1687-9643 .- 1687-9651. ; 2011
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we construct and verify the asymptotic expansion for the spectrum of a boundary-value problem in a unit circle periodically perforated along the boundary. It is assumed that the size of perforation and the distance to the boundary of the circle are of the same smallness. As an application of the obtained results the asymptotic behavior of the best constant in a Friedrichs-type inequality is investigated.
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| 8. |
- Koroleva, Yulia, et al.
(författare)
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On Friedrichs-type inequalities in domains rarely perforated along the boundary
- 2011
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Ingår i: Journal of inequalities and applications. - 1025-5834 .- 1029-242X. ; 2011
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Tidskriftsartikel (refereegranskat)abstract
- 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 $H^{1}$.
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