Jonathan J. Bevan

A Condition for the Hölder Regularity of Local Minimizers of a Nonlinear Elastic Energy in Two Dimensions

AbstractWe prove the local Hölder continuity of strong local minimizers of the stored energy functional

Austenite as a Local Minimizer in a Model of Material Microstructure with a Surface Energy Term

E(u)=\int_{\Omega}\lambda |\nabla u|^{2}+h({\rm det} \nabla u)\,{\rm d}x

An example of a C1,1 polyconvex function with no differentiable convex representative

E(u)=∫Ωλ|∇u|2+h(det∇u)dxsubject to a condition of ‘positive twist’. The latter turns out to be equivalent to requiring that u maps circles to suitably star-shaped sets. The convex function h(s) grows logarithmically as

A hydrostatic model of the Wirtz pump

{s\to 0+}

Minimizers with topological singularities in two dimensional elasticity

s→0+, linearly as