7 citations · 8 across the 8 of their papers we have counts for
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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…
A uniqueness criterion and a counterexample to regularity in an incompressible variational problem
Marcel Dengler, Jonathan J. Bevan
In this paper we consider the problem of minimizing functionals of the form in a suitably prepared class of incompressible, planar maps $u: B \righ…
A calibration method for estimating critical cavitation loads from below in 3D nonlinear elasticity
Jonathan J. Bevan, Jonathan H. B. Deane
In this paper we give an explicit sufficient condition for the affine map to be the global energy minimizer of a general class of elastic stored-energy functionals $I(…
Twists and shear maps in nonlinear elasticity: explicit solutions and vanishing Jacobians
Jonathan J. Bevan, Sandra Kabisch
In this paper we study constrained variational problems that are principally motivated by nonlinear elasticity theory. We examine in particular the relationship between the positiv…
A condition for the Holder regularity of strong local minimizers of a nonlinear elastic energy in two dimensions
Jonathan J. Bevan
We prove the local Hölder continuity of strong local minimizers of the stored energy functional \[E(u)=\int_{\om}λ|\nabla u|^{2}+h(\det \nabla u) \,dx\] subject to a condition of `…
Local minimizers and low energy paths in a model of material microstructure with a surface energy term
J. J. Bevan
A family of integral functionals F which, in a simplified way, model material microstructure occupying a two-dimensional domain D and which take account of surface energy and a var…