Approximation of planar Sobolev W^2,1 homeomorphisms by Piecewise\n Quadratic Homeomorphisms and Diffeomorphisms

2020/08/13 by Daniel Campbell, Campbell, Daniel, Stanislav Hencl +1 · 1 citation
Mathematics · #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2008.05736

Abstract

Given a Sobolev homeomorphism f\∈ W^2,1 in the plane we find a piecewise\nquadratic homeomorphism that approximates it up to a set of \ε measure.\nWe show that this piecewise quadratic map can be approximated by\ndiffeomorphisms in the W^2,1 norm on this set.\n

Citations

• Theories of elasticity with couple-stress
• Elastic materials with couple-stresses
• Convexity conditions and existence theorems in nonlinear elasticity

Cited by

• Diffeomorphic approximation of piecewise affine homeomorphisms

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