Conformally invariant variational integrals

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

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

Conformally invariant variational integrals
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by S. Granlund, P. Lindqvist and O. Martio PDF

Trans. Amer. Math. Soc. 277 (1983), 43-73 Request permission

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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