Sufficient conditions for regularity of area-preserving deformations |
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Authors: | Aram L Karakhanyan |
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Institution: | 1. School of Mathematics, The University of Edinburgh and, Maxwell Institute, James Clerk Maxwell Building, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland, UK
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Abstract: | We discuss some basic regularity properties of the area-preserving deformations ${u:\Omega \mapsto \mathbb{R}^2}$ that have minimal elastic energy ${\int \limits_\Omega|\nabla u|^2}$ among a suitable class of admissible vectorfields defined on a smooth, bounded domain ${\Omega\subset \mathbb{R}^2}$ . Although we restrict ourselves to the quadratic stored energy function and 2-space, most of our results extend to three dimensional setting with convex stored energy function. |
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