Timeline for Chain rule for weakly differentiable functions

5 events

when toggle format	what		by	license	comment
Oct 21, 2018 at 9:08	vote	accept	Mark Peletier
Dec 28, 2015 at 9:16	answer	added	leo monsaingeon		timeline score: 1
Jun 17, 2015 at 15:31	comment	added	Mark Peletier		$\nabla f = h$ is intended in the sense of distributions, i.e. $\int f \mathrm{div}\, \phi = -\int h \phi$ for all smooth compactly supported $\phi$.
Jun 17, 2015 at 15:06	comment	added	Juhana Siljander		What do you mean by $\nabla f$ if $f$ is merely in $L^1$? Or is it that you want to prove that under your assumptions $f$, in fact, has a Sobolev gradient and that it satisfies this formula? If $f \nabla \log f$ is well-defined under your assumptions, you could define that $\nabla f := f \nabla \log f$, if the Sobolev gradient does not exist otherwise. Such procedures can be found in the literature; of course, whether this makes any sense, depends on what you want to do,.
Jun 17, 2015 at 14:52	history	asked	Mark Peletier	CC BY-SA 3.0