Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak convergence of the sequences of homogeneous Young measures
  associated with a class of oscillating functions   We take under consideration Young measures with densities. The notion of
density of a Young measure is introduced and illustrated with examples. It is
proved that the density of a Young measure is weakly sequentially closed set.
In the case when density of a Young measure is a singleton (up to the set of
null measure), it is shown that the strong closedness (in rca(K)) of the set of
such measures, associated with Borel functions with values in the compact set K
? Rl, is equivalent with the strong closedness (in L1(K)) of the set of their
densities, provided the set K is convex. For an m-oscillating function the
notion of a total slope is proposed. It turns out, that if the total slopes of
the elements of the sequence of oscillating functions form monotonic sequence,
then the sequence of the respective (homogeneous) Young measures is weakly
convergent in rca(K). The limit is a homogeneous Young measure with the density
being the weak L1 sequential limit of the densities of the underlying Young
measures.

25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys