Abstract
Given a Sobolev homeomorphism f ∈ W2,1 in the plane we find a piecewise quadratic homeomorphism that approximates it up to a set of ε measure. We show that this piecewise quadratic map can be approximated by diffeomorphisms in the W2,1 norm on this set.
Funder
Grantová Agentura České Republiky
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering
Reference29 articles.
1. Ambrosio L.,
Fusco N. and
Pallara D., Functions of bounded variation and free discontinuity problems.
Oxford Mathematical Monographs.
The Clarendon Press, Oxford University Press,
New York
(2000).
2. Convexity conditions and existence theorems in nonlinear elasticity
3. The calculus of variations and materials science
4. Ball J.M., Singularities and computation of minimizers for variational problems, Foundations of computational mathematics (Oxford, 1999).
London Math. Soc. Lecture Note Ser. 284,
Cambridge Univ. Press,
Cambridge
(2001) 1–20.
5. Ball J.M., Progress and puzzles in Nonlinear Elasticity, Proceedings of course on Poly-, Quasi- and Rank-One Convexity in Applied Mechanics.
CISM Courses and Lectures.
Springer
(2010).