Global higher integrability of Jacobians on bounded domains
Let \(\Omega\) be a bounded domain. The authors give conditions for a vector-valued function in the Sobolev space \(W^{1,n}(\Omega ,{\mathbb R}^n)\) satisfying that \(\det Du(x)\geq 0\) on \(\Omega\) implies \(\det Du(x)\) is globally higher integrable on \(\Omega\). Also a condition that is sufficient to imply that \(\det Du(x)\) belongs to the Hardy space \(h^{1}_{z}(\Omega)\) is given.
scientific article; zbMATH DE number 1471448
scientific article