Jonathan J. Bevan

collaborators

2 papers

math.AP2024

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

Jonathan Bevan, Martin Kružík, Jan Valdman

Let $D (u)$ be the Dirichlet energy of a map $u$ belonging to the Sobolev space $H_{u_{0}}^{1} (Ω; R^{2})$ and let $A$ be a subclass of $H_{u_{0}}^{1} (Ω; R^{2})$ whose m…

math.AP2023

Hadamard's inequality in the mean

Jonathan Bevan, Martin Kružík, Jan Valdman

Let $Q$ be a Lipschitz domain in $R^{n}$ and let $f \in L^{\infty} (Q)$ . We investigate conditions under which the functional $$I_n(φ)=\int_Q |\nabla φ|^n+ f(x)\,\mathrm{det}…