A few remarks about Young measure swith densities

• Autorzy: Puchała Piotr

Identyfikatory

DOI

10.17512/jamcm.2025.4.05

• Języki publikacji: EN

Abstrakty

EN

We introduce the notion of a density of a Young measure and investigate its first properties. The notion is illustrated with examples of nonhomogeneous Young measures with densities, also providing a link between Young measures and set-valued analysis via the Bressan-Colombo-Fryszkowski theorem on the existence of continuous selections of multifunctions with decomposable values.

Słowa kluczowe

EN

Young measure; density; multifunction; continuous selection

PL

miara Younga; gęstość; wielofunkcyjność; selekcja ciągła

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2025
• Tom: Vol. 24, nr 4
• Strony: 75--84
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Puchała Piotr

• Department of Mathematics, Czestochowa University of Technology Czestochowa, Poland

Bibliografia

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• [2] Puchała, P. (2024). Certain convergence results for homogeneous Young measures with densities. J. Appl. Math. Comput. Mech., 23(4), 101-111.
• [3] Rindler, P. (2018). Calculus of Variations. Springer International Publishing AG, part of Springer Nature.
• [4] Puchała, P. (2017). A simple characterization of homogeneous Young measures and weak L1 convergence of their densities. Optimization, 66(2), 197-203.
• [5] Florescu, L.C., & Godet-Thobie, Ch. (2012). Young Measures and Compactness in Measure Spaces, Walter de Gruyter GmbH & Co. KG.
• [6] Kružík, M., & Roubícek, T. (2019). Mathematical Methods in Continuum Mechanics of Solids. Springer Nature.
• [7] Azhmyakov, V. (2019). A Relaxation-Based Approach to Optimal Control of Hybrid and Switched Systems. A practical guide for engineers. Elsevier Inc.
• [8] Pedregal, P. (2000). Variational Methods in Nonlinear Elasticity. Society for Industrial and Applied Mathematics.
• [9] Puchała, P. (2021). Young measures - an abstract tool in investigation concrete problems. In: Selected Topics in Contemporary Mathematical Modeling. Cze¸stochowa: Publishing Office of Czestochowa University of Technology, 91-105.
• [10] Fryszkowski, A. (2004). Fixed point theory for decomposable sets. Topological Fixed Point Theory and its Applications, vol. 2. Dordrecht, Boston, London: Kluwer Academic Publishers.
• [11] Hu, S., & Papageorgiou, N.S. (1997). Handbook of Multivalued Analysis. Vol. I. Theory, Mathe matics and its Applications, Vol. 419. Dordrecht, Boston, London: Kluwer Academic Publishers.
• [12] Arutyunov, A.A., & Obukhovskii, V. (2016). Convex and Set-Valued Analysis. Selected Topics. De Gruyter.
• [13] Obukhovskii, V., & Gel’man, B. (2020). Multivalued Maps and Differential Inclusions. World Scientific.
• [14] Repovš, D., & Semenov, P.V. (1998). Continuous Selections of Multivalued Mappings. Mathe matics and its Applications, Vol. 455. Dordrecht, Boston, London: Kluwer Academic Publishers.
• [15] Lin, P-K. (2004). Köthe-Bochner Function Spaces. New York: Springer Science+Business Media.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2026).