Sufficient conditions for regularity of area-preserving deformations |
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Authors: | Aram L. Karakhanyan |
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Affiliation: | 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 ${Omegasubset mathbb{R}^2}$ . 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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