Heat flow into spheres for a class of energies
Published in:
 Variational Problems in Riemannian Geometry.  2004, p. 4564
English
Let M and N be compact smooth Riemannian manifolds without boundaries. Then, for a map u : M→N, we consider a class of energies which includes the popular Dirichlet energy and the more general penergy. Geometric or physical questions motivate to investigate the critical points of such an energy or the corresponding heat flow problem. In the case of the Dirichlet energy, the heat flow problem has been intensively studied and is well understood by now. However, it has turned out that the case of the penergy (p≠2) is much more difficult in many respects. We give a survey of the known results for the pharmonic flow and indicate how these results can be extended to a larger class of energy types by using Young measure techniques which have recently been developed for quasilinear problems.

Faculty
 Faculté des sciences et de médecine

Department
 Département de Mathématiques

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Mathematics

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https://folia.unifr.ch/unifr/documents/299727
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