Newton and Bouligand derivatives of the scalar play and stop operator

2016/07/25 by Martin Brokate, Brokate, Martin
Mathematics · #47H30 #47J40 #49J52 #49M15 #58C20 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47H30 #msc:47J40 #msc:49J52 #msc:49M15 #msc:58C20

paper · pdf · doi:10.48550/arxiv.1607.07344

arxiv created 2019/04/16 · arxiv updated 2019/04/17

Abstract

We prove that the play and the stop operator possess Newton and Bouligand derivatives, and exhibit formulas for those derivatives. The remainder estimate is given in a strenghtened form, and a corresponding chain rule is developed. The construction of the Newton derivative ensures that the mappings involved are measurable.

Related

• Computing the Bouligand derivative of a class of piecewise-differentiable flows
• Value distribution and linear operators
• The Natural Chain of Binary Arithmetic Operations and Generalized Derivatives
• Remark on the Chain rule of fractional derivative in the Sobolev framework
• Sharp nonlinear estimates for multiplying derivatives of positive definite tensor fields