Deformations with smallest weighted L-p average distortion and Nitsche-type phenomena

作者：Martin Gaven J^*; McKubre Jordens Maarten

来源：Journal of the London Mathematical Society-Second Series, 2012, 85: 282-300.

DOI：10.1112/jlms/jdr042

The existence and uniqueness properties for extremal mappings with smallest weighted L-p distortion between annuli and the related Grotzsch-type problems are discussed. An interesting critical phase-type phenomenon is observed. When p %26lt; 1, apart from the identity map (and up to rotation), minimizers never exist. When p=1, we observe Nitsche-type phenomena; minimizers exist within a range of conformal moduli determined by properties of the weight function and not otherwise. When p %26gt; 1 minimizers always exist, regardless of the weight function. Interpreting the weight function as a density or %26apos;thickness profile%26apos; leads to interesting models for the deformation of highly elastic bodies and tearing-type phenomena.

• 出版日期2012-4