Fonction convexe d’une mesure (Convex function of a measure). (French) Zbl 0585.73063

Hadhri, Taïeb

C. R. Acad. Sci., Paris, Sér. I 301, 687-690 (1985).

Generalizing some previous works by Temam and co-workers [e.g. R. Temam and F. Demengel, Semin. Goulaouic-Meyer-Schwartz, Equations Deriv. Partielles 1982-1983, Exp. 10, 13 p. (1983; Zbl 0522.28002) and R. Temam, Can. Math. Bull. 25, 392-413 (1982; Zbl 0507.49011)], the author proposes the definition of a convex function of a measure which can be used to formulate mathematical problems in solid mechanics in inhomogeneous materials (e.g., in thermo-elastoplasticity). This is the new point. The local dependence of the resulting bounded Radon measure is studied. The proofs briefly given make use of Radon measure theory and Lebesgue’s decomposition.

Reviewer: G.A.Maugin

MSC:

74C99	Plastic materials, materials of stress-rate and internal-variable type
28A20	Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
28A10	Real- or complex-valued set functions
74E05	Inhomogeneity in solid mechanics

Keywords:

elasto-plasticity; functional framework; convex function of a measure; local dependence; bounded Radon measure; Lebesgue’s decomposition

Citations:

Zbl 0547.73026; Zbl 0522.28002; Zbl 0507.49011