Numerical Analysis Seminars: 'Positive twist' and Hölder regularity of local minimizers in planar, nonlinear elasticity
13 November 2015 14:00 in CM105
We prove the local Hölder continuity of strong local minimizers of integral functionals which represent the stored-energy of a two-dimensional elastic body. The physical requirement that elastic material is not permitted to interpenetrate during a deformation is the principal obstacle to proving these sorts of regularity results. To overcome it we impose a condition of 'positive twist', which is equivalent to requiring that deformations map circles to star-shaped sets, and which allows us to adapt and then apply some well-known elliptic regularity theory.
Contact David.Bourne@durham.ac.uk for more information