Conformally invariant variational integrals

Granlund, S.; Lindqvist, P.; Martio, O.

doi:10.1090/S0002-9947-1983-0690040-4

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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
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 . Obstacle problems and their connection to subextremals are studied. If is an extremal or a subextremal of , then $u \circ f$ is again an extremal or a subextremal if an appropriate change in is made.

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