On a certain embedding in the space of measures

• Autorzy: Puchała Piotr

Identyfikatory

DOI

10.17512/jamcm.2021.2.05

• Języki publikacji: EN

Abstrakty

EN

We take under consideration Young measures - objects that can be interpreted as generalized solutions of a class of certain nonconvex optimization problems arising among others in nonlinear elasticity or micromagnetics. They can be looked at from several points of view. We look at Young measures as at a class of weak* measurable, measure-valued mappings and consider the basic existence theorem for them. On the basis of this theorem, an imbedding of the set of bounded Borel functions into the set of Young measures is defined. Using the weak* denseness of the set of Young measures associated with simple functions in the set of Young measures, it is shown that this imbedding assigns the Young measure associated with any bounded Borel function.

Słowa kluczowe

EN

Young measures; optimization; engineering

PL

optymalizacja; inżynieria; funkcja Borela; miara Younga

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2021
• Tom: Vol. 20, nr 2
• Strony: 53--63
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Puchała Piotr

• Institute of Mathematics, Czestochowa University of Technology, Częstochowa, Poland

Bibliografia

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• [7] Pedregal, P. (1997). Parametrized Measures and Variational Principles. Birkhäuser.
• [8] Puchała, P. (2017). A simple characterization of homogeneous Young measures and weak L1 convergence of their densities. Optimization, 66(2), 197-203.
• [9] Puchała, P. (2014). An elementary method of calculating Young measures in some special cases. Optimization, 63(9), 1419-1430.
• [10] Balder, E.J. (1997). Consequences of denseness of Dirac Young measures. Journal of Mathematical Analysis and Applications, 207, 536-540.
• [11] Kružík, M., & Prohl, A. (2001). Young measure approximation in micromagnetics. Numerische Mathematik, 90, 291-307.
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• [14] De Philippis, G., & Rindler, F. (2017). Characterization of generalized Young measures generated by symmetric gradients. Archive for Rational Mechanics and Analysis, 224, 1087-1125.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).