Approximation by maps with nonnegative Jacobian (Q1947798)

The author studies the following problem: Let \(\Omega\subset{\mathbb R}^2\) be a bounded domain with piecewice smooth Jordan boundary. What conditions on a continuous map \(f: \bar\Omega \to {\mathbb R}^2\) ensure the possibility of approximating \(f\) arbitrarily well by continuously differentiable maps with a nonnegative Jacobian. The author gives some sufficient and necessary conditions for this problem.