Gradient Young measures generated by quasiconformal maps in the plane

2014/09/04 by Barbora Benešová, Benešová, Barbora, Malte Kampschulte +1
Mathematics · Materials Science · Computer Science · #Analytic and geometric function theory #Shape Memory Alloy Transformations #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.1409.1552

Abstract

In this contribution, we completely and explicitly characterize Young measures generated by gradients of quasiconformal maps in the plane. By doing so, we generalize the results of Astala and Faraco \citeAstalaFaraco who provided a similar result for quasiregular maps and Benešová and Kružík \citebbmk2013 who characterized Young measures generated by gradients of bi-Lipschitz maps. Our results are motivated by non-linear elasticity where injectivity of the functions in the generating sequence is essential in order to assure non-interpenetration of matter.

Citations

• The boundary correspondence under quasiconformal mappings
• Fine phase mixtures as minimizers of energy

Related

• Quasiconvexity at the boundary and concentration effects generated by\n gradients
• Young measures supported on invertible matrices
• Differential inclusions and Young measures involving prescribed Jacobian
• Generalized \mathbfW^1,1-Young measures and relaxation of problems with linear growth
• Generalised Young Measures and characterisation of gradient Young Measures