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Differential Geometry, Calculus of Variations, and Their Applications

12 A PRIORI GROWTH AND HOLDER ESTIMATES FOR HARMONIC
MAPPINGS Halldrfr I. Elfasson / Faculty of Engineering and Science, University of
Iceland, Reykjavik, Iceland INTRODUCTION Let M and N be C°° Riemannian
manifolds, with M compact and of dimension n > 2. A natural extension of the
Dirichlet problem to mappings f : M — N consists in finding extremals to the
variation integral given by the so-called energy The corresponding Euler-
Lagrange equation can be ...