Implicit elliptic differential equations (Q1344276)

The author studies the implicit differential equation \(f(x,u,Du,Lu) = 0\), where \(x \in \Omega \subset \mathbb{R}^ n\), \(u \in \mathbb{R}^ m\), \(Du = (Du_ 1, \dots, Du_ m)\), \(Lu = (Lu_ 1, \dots, Lu_ m)\), and \(f\): \(\Omega \times \mathbb{R}^ m \times \mathbb{R}^{mn} \times \mathbb{R}^ m \to \mathbb{R}\) is given.