Extremal mappings of finite distortion and the Radon–Riesz property

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Date
2022-12-23
DOI
10.4171/RMI/1379
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EMS Press
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© 2022 Real Sociedad Matemática Española
CC BY 4.0
https://creativecommons.org/licenses/by/4.0/
Abstract
We consider Sobolev mappings f ∈ W 1;q(Ω; C), 1 < q < ∞, between planar domains Ω ⊂ ℂ. We analyse the Radon–Riesz property for polyconvex functionals of the form (Formula presented) and show that under certain criteria, which hold in important cases, weak convergence in Wloc1;q.(Ω) of (for instance) a minimising sequence can be improved to strong convergence. This finds important applications in the minimisation problems for mappings of finite distortion and the Lp and Exp-Teichmüller theories.
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Keywords
Quasiconformal, finite distortion, extremal mappings, calculus of variation
Citation
Martin G, Yao C. (2022). Extremal mappings of finite distortion and the Radon–Riesz property. Revista Matematica Iberoamericana. 38. 7. (pp. 2057-2068).
URI
https://mro.massey.ac.nz/handle/10179/71127
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