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  • 1. Abramovic, A.
    et al.
    Pecaric, J.
    Persson, Lars-Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied mathematics.
    Varosanec, S.
    General inequalities via isotonic subadditive functionals2007In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, no 1, p. 15-28Article in journal (Refereed)
    Abstract [en]

    In this manuscript a number of general inequalities for isotonic subadditive functionals on a set of positive mappings are proved and applied. In particular, it is pointed out that these inequalities both unify and generalize some general forms of the Hö̈lder, Popoviciu, Minkowski, Bellman and Power mean inequalities. Also some refinements of some of these results are proved.

  • 2. Almqvist, A.
    et al.
    Essel, E.
    Persson, Lars-Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied mathematics.
    Wall, P.
    Homogenization of the unstationary incompressible Reynolds equation2007In: Tribology International, ISSN 0301-679X, E-ISSN 1879-2464, Vol. 40, no 9, p. 1344-1350Article in journal (Refereed)
    Abstract [en]

    This paper is devoted to the effects of surface roughness during hydrodynamic lubrication. In the numerical analysis a very fine mesh is needed to resolve the surface roughness, suggesting some type of averaging. A rigorous way to do this is to use the general theory of homogenization. In most works about the influence of surface roughness, it is assumed that only the stationary surface is rough. This means that the governing Reynolds type equation does not involve time. However, recently, homogenization was successfully applied to analyze a situation where both surfaces are rough and the lubricant is assumed to have constant bulk modulus. In this paper we will consider a case where both surfaces are assumed to be rough, but the lubricant is incompressible. It is also clearly demonstrated, in this case that homogenization is an efficient approach. Moreover, several numerical results are presented and compared with those corresponding to where a constant bulk modulus is assumed to govern the lubricant compressibility. In particular, the result shows a significant difference in the asymptotic behavior between the incompressible case and that with constant bulk modulus.

  • 3. Chechkin, G.A.
    et al.
    Persson, Lars-Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied mathematics.
    Kuroleva, Y.O
    On the precise asymptotics of the constant in Friedrichś inequality for functions vanishing on a part of the boundary with microinhomogeneous structure2007In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2007Article in journal (Refereed)
    Abstract [en]

    We construct the asymptotics of the sharp constant in the Friedrich-type inequality for functions, which vanish on the small part of the boundary Γ1ɛ. It is assumed that Γ1ɛ consists of (1/δ)n−1 pieces with diameter of order O(ɛδ). In addition, δ=δ(ɛ) and δ→0 as ɛ→0.

  • 4. Jain, P.
    et al.
    Persson, Lars-Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied mathematics.
    Upreti, P.
    Inequalities and properties of some generalized Orlicz classes and spaces2007In: Acta Mathematica Hungarica, ISSN 0236-5294, E-ISSN 1588-2632, Vol. 117, no 1-2, p. 161-174Article in journal (Refereed)
    Abstract [en]

    We discuss and complement the knowledge about generalized Orlicz classes and Orlicz spaces X Φ obtained by replacing the space L 1 in the classical construction by an arbitrary Banach function space X. Our main aim is to focus on the task to study inequalities in such spaces. We prove a number of new inequalities and also natural generalizations of some classical ones (e.g., Minkowski’s, Hölder’s and Young’s inequalities). Moreover, a number of other basic facts for further study of inequalities and function spaces are included.

  • 5. Johansson, M.
    et al.
    Persson, Lars-Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied mathematics.
    Scales of equivalent integral conditions related to Hardy type inequalities with applications2007In: Eurasian Mathematical journal, ISSN 1061-0022, no 3, p. 22-31Article in journal (Refereed)
  • 6. Kufner, A.
    et al.
    Kuliev, K.
    Persson, Lars-Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied mathematics.
    Oguntuase, J.A
    Generalized weighted inequality with negative powers2007In: Journal of Mathematical Inequalities, ISSN 1846-579X, Vol. 1, no 2, p. 269-280Article in journal (Refereed)
    Abstract [en]

    In this paper necessary and sufficient conditions for the validity of the generalizedHardy inequality for the case −∞ < q p < 0 and 0 < p q < 1 are derived. Furthermore,some special cases are considered.

  • 7. Kufner, A.
    et al.
    Malingrad, L.
    Persson, Lars-Erik
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Applied mathematics.
    THE HARDY INEQUALITY. ABOUT ITS HISTORY AND SOME RELATED RESULTS2007Book (Other (popular scientific, debate etc.))
  • 8. Kuliev, K.
    et al.
    persson, Lars-Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied mathematics.
    An extension of Rothe´s method to noncylindrical domains2007In: Applications of Mathematics, ISSN 0862-7940, E-ISSN 1572-9109, Vol. 52, no 5, p. 365-389Article in journal (Refereed)
    Abstract [en]

    In this paper Rothe's classical method is extended so that it can be used to solve some linear parabolic boundary value problems in non-cylindrical domains. The corresponding existence and uniqueness theorems are proved and some further results and generalizations are discussed and applied.

  • 9. Oguntuase, J.
    et al.
    Okpoti, C.
    Persson, Lars-Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied mathematics.
    Allotey, F.
    Multidimensional Hardy type inequalities for p < 0 and 0 < p < 12007In: Journal of Mathematical Inequalities, ISSN 1846-579X, Vol. 1, no 1, p. 1-11Article in journal (Refereed)
    Abstract [en]

    In this paper we establish some new multidimensional Hardy type inequalities for thecases p < 0 and 0 < p < 1 . These inequalities complement, generalize and unify most of theexisting results of this type in the literature e.g. those in [4] and [9]. Some of the results are newalso for the one dimensional case.

  • 10. Oguntuase, J.
    et al.
    Persson, Lars-Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied mathematics.
    Levin-Cochran-Lee type inequalities involving many functions2007In: A. Razmadze Mathematical Institute. Proceedings, ISSN 1512-0007, Vol. 144, p. 107-118Article in journal (Refereed)
  • 11.
    Persson, Lars-Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied mathematics.
    Ggatishvili, A.
    Johansson, M.
    Okpoti, C.
    Characterization of embeddings in Lorentz spaces using a method of discretization and anti-discretization2007In: Bulletin of the Australian Mathematical Society, ISSN 0004-9727, E-ISSN 1755-1633, Vol. 76, no 1, p. 69-92Article in journal (Refereed)
  • 12.
    Persson, Lars-Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied mathematics.
    Kalybay, A.
    Oinarov, R.
    Spectral properties of a class of singular differential operators2007In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, no 3, p. 355-376Article in journal (Refereed)
  • 13.
    Persson, Lars-Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied mathematics.
    Nikolova, L.
    Ushakova, E.
    Wedestig, A.
    Weighted Hardy and Polya-Knopp inequalities with variable limits2007In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, no 3, p. 547-558Article in journal (Refereed)
  • 14.
    Persson, Lars-Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied mathematics.
    Oguntuase, J.
    Okpoti, C.
    Allotey, F.
    Weighted multi- dimensional Hardy type inequalities via Jensen´s inequality2007In: Proceedings of A. Razmadze Mathematical Institute, ISSN 1512-0007, Vol. 144, p. 91-105Article in journal (Refereed)
    Abstract [en]

    The authors prove that Jenson's inequality implies some sharp weighted multidimensional Hardy type inequalities. In particular, their results unify and further extend several results of this type in the literature including the recent results in [A. Čižmešija, J. E. Pečarić and L. E. Persson, J. Approx. Theory 125 (2003), no. 1, 74--84; MR2016841 (2004i:42017); S. Kaijser et al., Math. Inequal. Appl. 8 (2005), no. 3, 403--417; MR2148234 (2006c:26036); S. Kaijser, L. E. Persson and A. Öberg, J. Approx. Theory 117 (2002), no. 1, 140--151; MR1920123 (2003f:26037)]. The main result is obtained in Theorem 3.1. In Section 4, the authors show that some existing results are special cases of the theorems obtained in this paper.

  • 15.
    Persson, Lars-Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied mathematics.
    Stepanov, V.
    Wall, P.
    Some scales of equivalent weight characterizations of Hardy´s inequality: the case q < p2007In: Mathematical Inequalities & Applications, ISSN 1331-4343, Vol. 10, no 2, p. 267-279Article in journal (Refereed)
    Abstract [en]

    We consider the weighted Hardy inequality                                                1/q                            1/p                                       q                      ∞                                       ∞                             x                                                                 f p (x)v(x)dx                               f (t)dt   u(x)dx       C                    0      0                                0for the case 0 < q < p < ∞, p > 1 . The weights u(x) and v(x) for which this inequalityholds for all f (x)    0 may be characterized by the Mazya-Rosin or by the Persson-Stepanovconditions. In this paper, we show that these conditions are not unique and can be supplementedby some continuous scales of conditions and we prove their equivalence. The results for the dualoperator which do not follow by duality when 0 < q < 1 are also given.

  • 16.
    Persson, Lars-Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied mathematics.
    Ushakova, E.
    Some multi-dimensional Hardy type integral inequalities2007In: Journal of Mathematical Inequalities, ISSN 1846-579X, Vol. 1, no 3, p. 301-319Article in journal (Refereed)
    Abstract [en]

    In this paper we prove some new results concerning multi-dimensional Hardy typeintegral inequalities and also some corresponding limit P ́ lya–Knopp type inequalities.

1 - 16 of 16
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