Structure of Solutions of Variational Problems by Alexander J. Zaslavski

Author:Alexander J. Zaslavski
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

(3.47)

By (3.44),

(3.48)

It follows from (3.48), (3.47), and (3.46) that the sequence is bounded. Together with inequality (3.35) and Proposition 2.10 this implies that

(3.49)

Thus the sequence is bounded for any integer k ≥ 1. Together with Proposition 3.5, this implies that there exist a subsequence of and an a.c. function such that for each integer k ≥ 1, we have

(3.50)

(3.51)

It follows from (3.50) and (3.45) that

(3.52)

In view of (3.51), (3.49), (3.48), (3.47), and Proposition 3.8, for each integer k ≥ 1, we have

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