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:ΩR2R2u\:\text{:}\Omega \subset \mathbb{R}^{2}\rightarrow \mathbb{R}^{2} with u=0u = 0 on ∂Ω and

Du(x)O(2),a.e. xΩ.Du(x) \in \mathrm{O}(2),\:\text{a.e. }x \in \Omega .

Résumé

Nous construisons une solution explicite d'une inclusion différentielle où on cherche une application u:ΩR2R2u\:\text{:}\Omega \subset \mathbb{R}^{2}\rightarrow \mathbb{R}^{2} avec u=0u = 0 sur ∂Ω et

Du(x)O(2),p.p. xΩ.Du(x) \in \mathrm{O}(2),\:\text{p.p. }x \in \Omega .

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