Remarks on the Iwaniec-Šverak conjecture (Q2879955)

The main results of the article under review deal with sufficient conditions that guarantee discreteness and openness of a mapping of finite distortion with integrable \(n\)-energy. One theorem deals with the condition \(K_I \in L^p_{\text{loc}}(\Omega)\), where \(p>1\), another uses the assumption \(K_I \in L^1_{\text{loc}}(\Omega)\). Relevant examples of planar mappings with finite multiplicity are given, where the image of a square spirals around the origin. The authors show that the assumption \(K_O \in L^p(\Omega)\), \(p \geq 1\), is essential for finite multiplicity.