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On the existence of variations, possibly with pointwise gradient constraints

Published online by Cambridge University Press:  12 May 2007

Simone Bertone  and
Arrigo Cellina
Simone Bertone
Affiliation:
Dipartimento di Matematica e Applicazioni, Universitá degli Studi di Milano-Bicocca, Via R. Cozzi 53, 20125 Milano, Italy; simone.bertone@unimib.it; arrigo.cellina@unimib.it
Arrigo Cellina
Affiliation:
Dipartimento di Matematica e Applicazioni, Universitá degli Studi di Milano-Bicocca, Via R. Cozzi 53, 20125 Milano, Italy; simone.bertone@unimib.it; arrigo.cellina@unimib.it
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Abstract

We propose a necessary and sufficient condition about the existence of variations, i.e.,of non trivial solutions $\eta\in W^{1,\infty}_0(\Omega)$ to the differential inclusion $\nabla\eta(x)\in-\nabla u(x)+{\bf D}$ .

Keywords

Variationsdifferential inclusionsnecessary conditions

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 2 , April 2007 , pp. 331 - 342
Copyright
© EDP Sciences, SMAI, 2007

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