New applications of Hadamard-in-the-mean inequalities to incompressible variational problems

Jonathan Bevan, Martin Kružík, Jan Valdman

Let $\mathbb{D}(u)$ be the Dirichlet energy of a map $u$ belonging to the Sobolev space $H_{u_0}^1(\Omega ;{\mathbb{R}}^2)$ and let $A$ be a subclass of $H_{u_0}^1(\Omega ;{\mathbb{R}}^2)$ whose m…