An explicit solution to a system of implicit differential equations

Bernard Dacorogna; Paolo Marcellini; Emanuele Paolini

doi:10.1016/j.anihpc.2006.11.007

JournalsaihpcVol. 25, No. 1pp. 163–171

An explicit solution to a system of implicit differential equations

Bernard Dacorogna
Section de Mathématiques, EPFL, 1015 Lausanne, Switzerland
Paolo Marcellini
Dipartimento di Matematica, Universita di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy
Emanuele Paolini
Dipartimento di Matematica, Universita di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy

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Abstract

In this article we give an explicit solution to the vectorial differential inclusion where we have to find a map $u : Ω \subset R^{2} \to R^{2}$ with $u = 0$ on $\partial Ω$ and

D u (x) \in O (2), a.e. x \in Ω.

Résumé

Nous construisons une solution explicite d'une inclusion différentielle où on cherche une application $u : Ω \subset R^{2} \to R^{2}$ avec $u = 0$ sur $\partial Ω$ et

D u (x) \in O (2), p.p. x \in Ω.

Cite this article

Bernard Dacorogna, Paolo Marcellini, Emanuele Paolini, An explicit solution to a system of implicit differential equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008), no. 1, pp. 163–171

DOI 10.1016/J.ANIHPC.2006.11.007