Published online by Cambridge University Press: 15 December 2004
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.