Injective mappings and solvable vector fields of Euclidean spaces.
Let \(\Omega\) be an open connected subset of \(\mathbb{R}^n\) and let \(\Phi(\Omega)\) denote the subset of \(C^\infty(\Omega,\mathbb{R}^n)\) consisting of the mappings \(F\) having invertible derivative \(F'(x)\) for each \(x\in\Omega\). Under a generalized convexity condition, the injectivity of a mapping \(F\in \Phi(\Omega)\) for \(n=2\) and \(3\) is proved. Connections with global solvability of partial differential equations are discussed.
charateristics and global solvability of partial differential equations
scientific article; zbMATH DE number 2037258