Local mappings on spaces of differentiable functions
type: Item
instance of: scholarly article
title: Local mappings on spaces of differentiable functions
zbMATH Open document ID: 0808.46030
DOI: 10.1007/BF02568330
author: Giovanni Alberti
author: Giuseppe Buttazzo
published in: Manuscripta Mathematica
publication date: 1995-03-09T00:00:00Z
full work available at URL: https://eudml.org/doc/155826
review text: The authors prove that a functional \(F(u,B)\) defined for every \(C^ k\)- function \(u\in C^ k(\Omega;\mathbb{R}^ m)\) (for \(\Omega\) a bounded open subset in \(\mathbb{R}^ n\)) and every Borel subset \(B\) of \(\Omega\) under very mild assumptions admits an integral representation \[ F(u,B)= \int_ B f(x, D^ k u(x)) d\mu(x) \] for a suitable measure \(\mu\). Such integral representations are very important and have been widely studied. Earlier results on integral representation of functionals on spaces of differentiable maps needed additional hypotheses to work, typically growth conditions on the derivatives.
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 58D15
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 46G05
zbMATH DE Number: 492779
zbMATH Keywords: local mappings
zbMATH Keywords: spaces of differentiable functions
zbMATH Keywords: integral representation
reviewed by: Vagn Lundsgaard Hansen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 492779