Classicalexamples of moreand more oscillatingreal-valued functions on a domain N ?of R are the functions u (x)=sin(nx)with x=(x, ..., x ) or the so-called n 1 1 n n+1 Rademacherfunctionson]0,1 , u (x)=r (x) = sgn(sin(2 x))(seelater3.1.4). n n They may appear as the gradients?v of minimizing sequences (v ) in some n n n?N variationalproblems. Intheseexamples, thefunctionu convergesinsomesenseto n ameasure u on ? xR, called Young measure. In Functional Analysis formulation, this is the narrow convergence to u of the image of the Lebesgue measure on ? by ? ? (?, u (?)). In the disintegrated form...
Classicalexamples of moreand more oscillatingreal-valued functions on a domain N ?of R are the functions u (x)=sin(nx)with x=(x, ..., x ) or the so-ca...
Young measures are now a widely used tool in the Calculus of Variations, in Control Theory, in Probability Theory and other fields. They are known under different names such as "relaxed controls," "fuzzy random variables" and many other names.
This monograph provides a unified presentation of the theory, along with new results and applications in various fields. It can serve as a reference on the subject. Young measures are presented in a general setting which includes finite and for the first time infinite dimensional spaces: the fields of applications of Young measures (Control...
Young measures are now a widely used tool in the Calculus of Variations, in Control Theory, in Probability Theory and other fields. They are known ...
