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Certain convergence results for homogeneous young measures with densities

Puchała Piotr

Journal of Applied Mathematics and Computational Mechanics

2024

Vol. 23, nr 4

101-111

We consider Young measures associated with elements of sequences of m-oscillating functions. Such Young measures are homogeneous and absolutely continuous with respect to the Lebesgue measure. The total slope of an m-oscillating function is defined, and the basic property of a set of Young measures associated with m-oscillating functions is stated. Next, the relation between weak L1 convergence of densities and weak convergence, with respect to the total variation norm, of respective Young measures is investigated. The last result unifies and generalizes most examples of Young measures usually presented in the literature.