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A differential inclusion: the case of an isotropic set
Published online by Cambridge University Press: 15 December 2004
Abstract
In this article we are interested in the following problem: to find 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 a compact isotropic set of $\mathbb{R}^{2\times 2}$. We will show an existence theorem under suitable hypotheses on φ.
- 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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