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Superposition and Chain Rule for Bounded Hessian Functions

✍ Scribed by Giuseppe Savaré; Franco Tomarelli

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 579 KB
Volume: 140
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.1998.1770

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✦ Synopsis

We study the properties of superposition of Bounded Hessian functions, establishing the validity of a second-order chain rule. We prove rectifiability properties of all noncritical level sets of BH-functions by showing a geometric measure theory analogous of Dini's Theorem.

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## Abstract Let __I__, __J__ ⊂ ℝ be intervals. The main result says that if a superposition operator __H__ generated by a function of two variables __h__: __I__ × __J__ → ℝ, __H__ (__φ__)(__x__) ≔ __h__ (__x__, __φ__ (__x__)), maps the set __BV__ (__I__, __J__) of all bounded variation functions,