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- W2466658599 abstract "In this paper we introduce a new class of real-valued locally Lipschitz functions, (that are similar in nature and definition to Valadier's {sl saine} functions) which we call {sl arc-wise essentially smooth}, and we show that if $g : R^n rightarrow R$ is arc-wise essentially smooth on $R^n$ and each function $f_j : R^m rightarrow R, 1 leq j leq n$ is strictly differentiable almost everywhere in $R^m$, then $g circ f$ is strictly differentiable almost everywhere in $R^m$, where $f equiv (f_1,f_2, . . . f_n)$. We also show that all the semi-smooth and pseudo-regular functions are arc-wise essentially smooth. Thus, we provide a large and robust lattice algebra of Lipschitz functions whose generalized derivatives are well-behaved." @default.
- W2466658599 created "2016-07-22" @default.
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- W2466658599 date "1998-01-01" @default.
- W2466658599 modified "2023-09-26" @default.
- W2466658599 title "A chain rule for essentially strictly differentiable Lipschitz functions" @default.
- W2466658599 hasPublicationYear "1998" @default.
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