J. Valdman

activity

20132026

collaborators

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3 papers · 1 filter

math.AP2026

Sharp mean Hadamard inequalities and polyconvex integrands that give rise to convex functionals

Jonathan Bevan, Martin Kružík, Jan Valdman

We investigate several instances of the Hadamard inequality in the mean in two dimensions. As a consequence, we prove the uniqueness of minimizers of an integral functional with a…

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}…