Mappings of finite distortion: decay of the Jacobian (Q1930286)

The authors study continuous, discrete, and open mappings \(f:D \to {\mathbb R}^n\), \(D \subset {\mathbb R}^n\), and prove that the requirement for the outer dilatation \( K_O^{1/(n-1)}(\cdot {\,} ,f) \in L^p_{\text{loc}}(D)\) for some \(p \geq 1\) implies \[ \log(e+ 1/J(\cdot {\,},f)) \in L^p_{\text{loc}}(D). \] An example is given to demonstrate that the conclusion is sharp.