| 1. |
- Almanasreh, Hasan, 1981, et al.
(författare)
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G-convergence of Dirac operators : G-convergence of Dirac operators
- 2012
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965. ; 2012
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Tidskriftsartikel (refereegranskat)abstract
- We consider the linear Dirac operator with a (−1)-homogeneous locally periodic potential that varies with respect to a small parameter. Using the notation of G-convergence for positive self-adjoint operators in Hilbert spaces we prove G-compactness in the strong resolvent sense for families of projections of Dirac operators. We also prove convergence of the corresponding point spectrum in the spectral gap.
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| 2. |
- Almanasreh, Hasan, 1981, et al.
(författare)
-
G-convergence of Dirac operators
- 2012
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 1758-4965 .- 0972-6802. ; 2012, s. Article ID 789875, 13 pages-
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Tidskriftsartikel (refereegranskat)abstract
- We consider the linear Dirac operator with a (−1)-homogeneous locally periodic potential that varies with respect to a small parameter. Using the notation of G-convergence for positive self-adjoint operators in Hilbert spaces we prove G-compactness in the strong resolvent sense for families of projections of Dirac operators. We also prove convergence of the corresponding point spectrum in the spectral gap.
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| 3. |
- Almqvist, Andreas, et al.
(författare)
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Multiscale homogenization of a class of nonlinear equations with applications in lubrication theory and applications
- 2011
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965. ; 9:1, s. 17-40
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Tidskriftsartikel (refereegranskat)abstract
- We prove a homogenization result for monotone operators by using the method of multiscale convergence. More precisely, we study the asymptotic behavior as epsilon -> 0 of the solutions u(epsilon) of the nonlinear equation div a(epsilon)(x, del u(epsilon)) = div b(epsilon), where both a(epsilon) and b(epsilon) oscillate rapidly on several microscopic scales and a(epsilon) satisfies certain continuity, monotonicity and boundedness conditions. This kind of problem has applications in hydrodynamic thin film lubrication where the bounding surfaces have roughness on several length scales. The homogenization result is obtained by extending the multiscale convergence method to the setting of Sobolev spaces W-0(1,p)(Omega), where 1 < p < infinity. In particular we give new proofs of some fundamental theorems concerning this convergence that were first obtained by Allaire and Briane for the case p = 2.
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| 4. |
- Barza, Sorina, 1967-, et al.
(författare)
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Best constants between equivalent norms in Lorentz sequence spaces
- 2012
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965. ; 2012
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Tidskriftsartikel (refereegranskat)abstract
- We find the best constants in inequalities relating the standard norm, the dual norm, and the norm ‖ 푥 ‖ ( 푝 , 푠 ) ∑ ∶ = i n f { 푘 ‖ 푥 ( 푘 ) ‖ 푝 , 푠 } , where the infimum is taken over all finite representations ∑ 푥 = 푘 푥 ( 푘 ) in the classical Lorentz sequence spaces. A crucial point in this analysis is the concept of level sequence, which we introduce and discuss. As an application, we derive the best constant in the triangle inequality for such spaces.
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| 5. |
- Flodén, Liselott, 1967-, et al.
(författare)
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A strange term in the homogenization of parabolic equations with two spatial and two temporal scales
- 2012
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965. ; , s. Art. no. 643458-
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Tidskriftsartikel (refereegranskat)abstract
- We study the homogenization of a parabolic equation with oscillations in both space and time in the coefficient a((x/()),(t/²)) in the elliptic part and spatial oscillations in the coefficient ((x/())) that is multiplied with the time derivative ∂_{t}u^{}. We obtain a strange term in the local problem. This phenomenon appears as a consequence of the combination of the spatial oscillation in ((x/())) and the temporal oscillation in a((x/()),(t/²)) and disappears if either of these oscillations is removed.
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| 6. |
- Gogatishvili, Amiran S., et al.
(författare)
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Some new iterated Hardy-type inequalities
- 2012
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965.
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Tidskriftsartikel (refereegranskat)abstract
- We characterize the validity of the Hardy-type inequality ∫ s ∞ h (z) d z p, u, (0, t)q, w, (0, ∞) ≤ c h θ, v (0, ∞), where 0 < p < ∞, 0 < q ≤ ∞, 1 < θ ≤ ∞, u, w, and v are weight functions on (0, ∞). Some fairly new discretizing and antidiscretizing techniques of independent interest are used.
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| 7. |
- Kalybay, Aigerim A., et al.
(författare)
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Three weights higher order Hardy type inequalities
- 2006
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965. ; 4:2, s. 163-191
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the following three weights higher order Hardy type inequality (0.1) ‖g‖q,u≤ C‖Dρkg‖p,v where Dρi denotes the following weighted differential operator: {dig(t)dti,i=0,1,...,m−1,di−mdti−m(p(t)dmg(t)dtm),i=m,m+1,...,k, for a weight function ρ(⋅). A complete description of the weights u, v and ρ so that (0.1) holds was given in [4] for the case 1
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| 8. |
- Lukkassen, Dag, et al.
(författare)
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Mathematical analysis and homogenization of the torsion problem
- 2008
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965. ; 6:2, s. 155-176
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we address the limitations of the classical formulation of the torsion problem and give a self-contained survey of the function spaces and formulations that are more suitable for analysing the torsional behavior of composite materials. We also prove some homogenization results for the torsion problem in both the periodic and stochastic setting. Our theoretical results are illustrated by numerical examples.
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| 9. |
- Lukkassen, Dag, et al.
(författare)
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Reiterated homogenization of nonlinear monotone operators in a general deterministic setting
- 2009
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965. ; 7:2, s. 121-152
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Tidskriftsartikel (refereegranskat)abstract
- We study reiterated homogenization of a nonlinear non-periodic elliptic differential operator in a general deterministic setting as opposed to the usual stochastic setting. Our approach proceeds from an appropriate notion of convergence termed reiterated ∑-convergence. A general deterministic homogenization theorem is proved and several concrete examples are studied under various structure hypotheses ranging from the classical periodicity hypothesis to more complicated, but realistic, structure hypotheses.
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| 10. |
- Lukkassen, Dag, et al.
(författare)
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Two-scale convergence with respect to measures and homogenization of monotone operators
- 2005
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965. ; 3:2, s. 125-161
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Tidskriftsartikel (refereegranskat)abstract
- In 1989 Nguetseng introduced two-scale convergence, which now is a frequently used tool in homogenization of partial differential operators. In this paper we discuss the notion of two-scale convergence with respect to measures. We make an exposition of the basic facts of this theory and develope it in various ways. In particular, we consider both variable Lp spaces and variable Sobolev spaces. Moreover, we apply the results to a homogenization problem connected to a class of monotone operators.
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