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Stability of weakly almost conformal mappings


Authors: Baisheng Yan and Zhengfang Zhou
Journal: Proc. Amer. Math. Soc. 126 (1998), 481-489
MSC (1991): Primary 49J10, 35J50, 30C62
DOI: https://doi.org/10.1090/S0002-9939-98-04079-9
MathSciNet review: 1415344
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Abstract: We prove a stability of weakly almost conformal mappings in $W^{1, p}(\Omega;\mathbf {R}^n)$ for $p$ not too far below the dimension $ n$ by studying the $ W^{1, p}$-quasiconvex hull of the set $\mathcal C_n $ of conformal matrices. The study is based on coercivity estimates from the nonlinear Hodge decompositions and reverse Hölder inequalities from the Ekeland variational principle.


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Additional Information

Baisheng Yan
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: yan@math.msu.edu

Zhengfang Zhou
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: zfzhou@math.msu.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04079-9
Received by editor(s): February 26, 1996
Received by editor(s) in revised form: August 12, 1996
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1998 American Mathematical Society

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