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A few remarks on an embedding into the set of measures

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EN
Abstrakty
EN
We continue considerations concerning Young measures associated with bounded measurable functions from a recent article. We look at them as at the weak* measurable, measure-valued mappings. We show examples explaining that we cannot regard a Young measure (i.e. a weak* -measurable mapping) δu(x) as an explicit form of a Young measure associated with a function u. We also consider convergence of the sequences of Young measures.
Rocznik
Strony
77--85
Opis fizyczny
Bibliogr.15 poz.
Twórcy
  • Department of Mathematics, Czestochowa University of Technology Cze ̧stochowa, Poland
Bibliografia
  • [1] Puchała, P. (2021). On a certain embedding in the space of measures. J. Appl. Math. Comput. Mech., 20(2), 53-63.
  • [2] Dacorogna, B. (2008). Direct Methods in the Calculus of Variations. Springer Science+Business Media, LLC.
  • [3] Kružík, M., & Roubíček, T. (2019). Mathematical Methods in Continuum Mechanics of Solids. Springer Nature.
  • [4] Young, L.C. (1937). Generalized curves and the existence of an attained absolute minimum in the calculus of variations. Comptes Rendus de la Société des Sciences et des Lettres de Varsovie, classe III, 30, 212-234.
  • [5] Florescu, L.C., & Godet-Thobie, Ch. (2012). Young Measures and Compactness in Measure Spaces, Walter de Gruyter GmbH & Co. KG.
  • [6] Pedregal, P. (1997). Parametrized Measures and Variational Principles. Birkhäuser.
  • [7] Rindler, P. (2018). Calculus of Variations. Springer International Publishing AG, Part of Springer Nature.
  • [8] Roubíček, T. (1997). Relaxation in Optimization Theory and Variational Calculus. Walter de Gruyter.
  • [9] Müller, S. (1999). Variational Models for Microstructure and Phase Transitions. Calculus of variations and geometric evolution problems. Lecture Notes in Mathematics, (1713), Springer, 85-210.
  • [10] Pedregal, P. (2000). Variational Methods in Nonlinear Elasticity. Society for Industrial and Applied Mathematics.
  • [11] Puchała, P. (2014). An elementary method of calculating Young measures in some special cases. Optimization, 63(9), 1419-1430.
  • [12] Puchała, P. (2017). A simple characterization of homogeneous Young measures and weak L1 convergence of their densities. Optimization, 66(2), 197-203.
  • [13] Grzybowski, A.Z., & Puchała, P. (2019). Classical Young Measures Generated by Oscillating Sequences with Uniform Representation. Transactions on Engineering Technologies. Springer Nature Singapore Ptu Ltd., 1-12.
  • [14] Aliprantis, Ch.D., & Border, K.C. (1999). Infinite Dimensional Analysis. A Hitchhiker’s Guide. Berlin-Heidelberg: Springer-Verlag.
  • [15] Benedetto, J.J., & Czaja, W. (2009). Integration and Modern Analysis. Boston: Birkhäuser.
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Bibliografia
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bwmeta1.element.baztech-e22997f8-d8fc-4010-97da-957d9adb31d5
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