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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Conformally invariant variational integrals


Authors: S. Granlund, P. Lindqvist and O. Martio
Journal: Trans. Amer. Math. Soc. 277 (1983), 43-73
MSC: Primary 30C70; Secondary 49A21
DOI: https://doi.org/10.1090/S0002-9947-1983-0690040-4
MathSciNet review: 690040
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Abstract: Let $ f:G \to {R^n}$ be quasiregular and $ I = \int {F(x,\nabla \,u)\,dm} $ a conformally invariant variational integral. Hölder-continuity, Harnack's inequality and principle are proved for the extremals of $ I$. Obstacle problems and their connection to subextremals are studied. If $ u$ is an extremal or a subextremal of $ I$, then $ u \circ f$ is again an extremal or a subextremal if an appropriate change in $ F$ is made.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0690040-4
Keywords: Variational integrals, quasiregular mappings, subextremals
Article copyright: © Copyright 1983 American Mathematical Society