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  • 1.
    Almqvist, Andreas
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Burtseva, Evgeniya
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Ràfols, Francesc Pérez
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    New insights on lubrication theory for compressible fluids2019In: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 145, article id 103170Article in journal (Refereed)
    Abstract [en]

    The fact that the film is thin is in lubrication theory utilised to simplify the full Navier–Stokes system of equations. For incompressible and iso-viscous fluids, it turns out that the inertial terms are small enough to be neglected. However, for a compressible fluid, we show that the influence of inertia depends on the (constitutive) density-pressure relationship and may not always be neglected. We consider a class of iso-viscous fluids obeying a power-law type of compressibility, which in particular includes both incompressible fluids and ideal gases. We show by scaling and asymptotic analysis, that the degree of compressibility determines whether the terms governing inertia may or may not be neglected. For instance, for an ideal gas, the inertial terms remain regardless of the film height-to-length ratio. However, by means of a specific modified Reynolds number that we define we show that the magnitudes of the inertial terms rarely are large enough to be influential. In addition, we consider fluids obeying the well-known Dowson and Higginson density-pressure relationship and show that the inertial terms can be neglected, which allows for obtaining a Reynolds type of equation. Finally, some numerical examples are presented in order to illustrate our theoretical results.

  • 2.
    Burtseva, Evgeniya
    Luleå University of Technology, Department of Engineering Sciences and Mathematics.
    Operators and Inequalities in various Function Spaces and their Applications2016Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    This Licentiate thesis is devoted to the study of mapping properties of different operators (Hardy type, singular and potential) between various function spaces.

    The main body of the thesis consists of five papers and an introduction, which puts these papers into a more general frame.

    In paper A we prove the boundedness of the Riesz Fractional Integration Operator from a Generalized Morrey Space to a certain Orlicz-Morrey Space, which covers the Adams resultfor Morrey Spaces. We also give a generalization to the case of Weighted Riesz Fractional Integration Operators for a class of weights.

    In paper B we study the boundedness of the Cauchy Singular Integral Operator on curves in complex plane in Generalized Morrey Spaces. We also consider the weighted case with radial weights. We apply these results to the study of Fredholm properties of Singular Integral Operators in Weighted Generalized Morrey Spaces.

    In paper C we prove the boundedness of the Potential Operator in Weighted Generalized Morrey Spaces in terms of Matuszewska-Orlicz indices of weights and apply this result to the Hemholtz equation with a free term in such a space. We also give a short overview of some typical situations when Potential type Operators arise when solving PDEs.

    ​In paper D some new inequalities of Hardy type are proved. More exactly, the boundedness of multidimensional Weighted Hardy Operators in Hölder Spaces are proved in cases with and without compactification.

    In paper E the mapping properties are studied for Hardy type and Generalized Potential type Operators in Weighted Morrey type Spaces.

  • 3.
    Burtseva, Evgeniya
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Singular Integral Operators in Generalized Morrey Spaces on Curves in the Complex Plane2017In: Mediterranean Journal of Mathematics, ISSN 1660-5446, E-ISSN 1660-5454, Vol. 14, no 5, article id 203Article in journal (Refereed)
    Abstract [en]

    We study the boundedness of the Cauchy singular integral operators on curves in complex plane in generalized Morrey spaces. We also consider the weighted case with radial weights. We apply these results to the study of Fredholm properties of singular integral operators in weighted generalized Morrey spaces.

  • 4.
    Burtseva, Evgeniya
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Lundberg, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Arctic University of Norwa.
    Samko, Natasha
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Multi–dimensional Hardy type inequalities in Hölder spaces2018In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 12, no 3, p. 719-729Article in journal (Refereed)
    Abstract [en]

    Most Hardy type inequalities concern boundedness of the Hardy type operators in Lebesgue spaces. In this paper we prove some new multi-dimensional Hardy type inequalities in Hölder spaces.

  • 5. Burtseva, Evgeniya
    et al.
    Lundberg, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Potential type operators in PDEs and their applications2017In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1798, article id 020178Article in journal (Refereed)
    Abstract [en]

     We prove the boundedness of Potential operator in weighted generalized Morrey space in terms of Matuszewska-Orlicz indices of weights and apply this result to the Hemholtz equation in r3 with a free term in such a space. We also give a short overview of some typical situations when Potential type operators arise when solving PDEs.

  • 6.
    Burtseva, Evgeniya
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Arctic University of Norway, Narvik, Norway.
    Samko, Natasha
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Necessary and sufficient conditions for the boundedness of weighted Hardy operators in Hölder spaces2018In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 291, no 11-12, p. 1655-1665Article in journal (Refereed)
    Abstract [en]

    We study one‐ and multi‐dimensional weighted Hardy operators on functions with Hölder‐type behavior. As a main result, we obtain necessary and sufficient conditions on the power weight under which both the left and right hand sided Hardy operators map, roughly speaking, functions with the Hölder behavior only at the singular point to functions differentiable for and bounded after multiplication by a power weight. As a consequence, this implies necessary and sufficient conditions for the boundedness in Hölder spaces due to the corresponding imbeddings. In the multi‐dimensional case we provide, in fact, stronger Hardy inequalities via spherical means. We also separately consider the case of functions with Hölder‐type behavior at infinity (Hölder spaces on the compactified ).

  • 7.
    Burtseva, Evgeniya
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On weighted generalized fractional and Hardy-type operators acting between Morrey-type spaces2017In: Fractional Calculus and Applied Analysis, ISSN 1311-0454, E-ISSN 1314-2224, Vol. 20, no 6, p. 1545-1566Article in journal (Refereed)
    Abstract [en]

    We study weighted generalized Hardy and fractional operators acting from generalized Morrey spaces Lp,φ,(n) into Orlicz-Morrey spaces LΦ,φ,(n). We deal with radial quasi-monotone weights and assumptions imposed on weights are given in terms of Zigmund-type integral conditions. We find conditions on φ,Φ, the weight w and the kernel of the fractional operator, which insures such a boundedness. We prove some pointwise estimates for weighted generalized fractional operators via generalized Hardy operators, which allow to obtain the weighted boundedness for fractional operators from those for Hardy operators. We provide also some easy to check numerical inequalities to verify the obtained conditions.

  • 8.
    Burtseva, Evgeniya
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Weighted Adams type theorem for the Riesz fractional integral in generalized Morrey Space2016In: Fractional Calculus and Applied Analysis, ISSN 1311-0454, E-ISSN 1314-2224, Vol. 19, no 4, p. 954-972Article in journal (Refereed)
    Abstract [en]

    We prove the boundedness of the Riesz fractional integration operator from a generalized Morrey space L-p,L-phi to a certain Orlicz-Morrey space L-Phi,L-phi which covers the Adams result for Morrey spaces. We also give a generalization to the case of weighted Riesz fractional integration operators for some class of weights.

1 - 8 of 8
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