General method of relaxation. [Pt. 1], Functionals defined on BD(Omega) space

• Autorzy: Bojarski J.
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to find the lower semicontinuous regularization of a functional of displacement energy, with a constrains on the boundary of Omega. This functional describes the elasto-perfectly plastic energy of a solid made of a nonhomogeneous (or homogeneous) Hencky material. In this contribution we prove that the mentioned above regularization is equal to the relaxation found in [4], i.e. B** = B#*.

Słowa kluczowe

EN

BD space; convex normal integrand; duality theory; lower semicontinuous regularization; polifunctions

PL

metoda relaksacji; optymalizacja; rachunek wariacyjny; sterowanie optymalne; teoria dwoistości

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 3
• Strony: 289--301
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Bojarski J.

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, 00-049 Warszawa, Poland

Bibliografia

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• [3] P. Aviles, Y. Giga, Variational integrals on mappings of bounded variation and their lower semicontinuity, Arch. Rational Mech. Anal., 115 (1991) 201-255.
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• [5] N. Dunford, J. T. Schwar z, Linear Operators, Part I, Interscie.nce Publishers, New York 1958.
• [6] I. Ekeland, R. Temam, Convex Analysis and Variational Problems, North Holland, Amsterdam, New York 1976.
• [7] R. Engelking, General Topology, Państwowe Wydawnictwo Naukowe, Warszawa 1977.
• [8] I. Fonseca, S. Müller, Relaxation of guasiconvexfunctionals in BV(12, RP) for integrands f (x, u, Vu), Arch. Rational Mech. Analysis, 123 (1993) 1-49.
• [9] E. Giusti, Minimal Surfaces and Functions of Bounded Variation, in: Lecture Notes Written by G. H. Williams, Dep. Math., Australian National University, Canberra 10 (1977).
• [10] R. Kohn, R. Temam, Dual spaces of stresses and strains with applications to Hencky plasticity, Appl. Math. Optim., 10 (1983) 1-35.
• [11] R. Temam, Mathematical Problems in Plasticity, Gauthier-Villars, Paris and Trans-Inter-Scienta, Toubridge 1985.
• [12] R. Temam, G. Strang, Functions of bounded deformation, Arch. Rational Mech. Analysis, 75 (1980) 7-21.