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A differential inclusion: the case of an isotropic set

Published online by Cambridge University Press:  15 December 2004

Gisella Croce
Gisella Croce*
Affiliation:
Département de Mathématiques, EPFL, 1015 Lausanne, Switzerland; [email protected]
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Abstract

In this article we are interested in the following problem: tofind a map $u: \Omega \to \mathbb{R}^2$ that satisfies $$\left\{\begin{array}{ll}D u \in E\,\, &\mbox{{\it a.e.} in } \Omega\\ u(x)=\varphi(x) &x \in \partial \Omega\end{array}\right.$$ where Ω is an open set of $\mathbb{R}^2$ and E is acompact isotropic set of $\mathbb{R}^{2\times 2}$ . We will show anexistence theorem under suitable hypotheses on φ.

Keywords

Rank one convex hullpolyconvex hulldifferentialinclusionisotropic set.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 1 , January 2005 , pp. 122 - 138
Copyright
© EDP Sciences, SMAI, 2005

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References

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