1 results
A differential inclusion: the case of an isotropic set
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- Journal:
- ESAIM: Control, Optimisation and Calculus of Variations / Volume 11 / Issue 1 / January 2005
- Published online by Cambridge University Press:
- 15 December 2004, pp. 122-138
- Print publication:
- January 2005
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- Article
- Export citation
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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.
