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In mathematical analysis, a Young measure is a parameterized measure that is associated with certain subsequences of a given bounded sequence of measurable functions. They are a quantification of the oscillation effect of the sequence in the limit. Young measures have applications in the calculus of variations, especially models from material science, and the study of nonlinear partial differential equations, as well as in various optimization (or optimal control problems). They are named after Laurence Chisholm Young who invented them, already in 1937 in one dimension (curves) and later in higher dimensions in 1942.[1]
Young measures provide a solution to Hilbert’s twentieth problem, as a broad class of problems in the calculus of variations have solutions in the form of Young measures.[2]
- ^ Young, L. C. (1942). "Generalized Surfaces in the Calculus of Variations". Annals of Mathematics. 43 (1): 84–103. doi:10.2307/1968882. ISSN 0003-486X. JSTOR 1968882.
- ^ Balder, Erik J. "Lectures on Young measures." Cahiers de Mathématiques de la Décision 9517 (1995).