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The regularity of monotone maps of finite compression

✍ Scribed by Luis A. Caffarelli

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 428 KB
Volume: 50
Category: Article
ISSN: 0010-3640
DOI: 10.1002/(sici)1097-0312(199706)50:6<563::aid-cpa2>3.0.co;2-6

No coin nor oath required. For personal study only.

✦ Synopsis

1 scalars control the (n × n)-dimensional matrix Dv). For instance, typical theorems are: THEOREM 0.1 If v is bounded and div v and curl v belong to C k, α (or W k, p ), so does all of Dv, and its C k, α (or W k, p ) norm is controlled by that of div and curl.

Another form of the same theorem is the following:

and v 1 , v 2 are in the same functional space as v, with appropriate bounds.

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