J. Valdman

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20242026

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math.AP2026

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

Jonathan Bevan, Martin KruÅ¾Ãk, 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 KruÅ¾Ãk, Jan Valdman

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