Faculté des sciences et de médecine

Heat flow into spheres for a class of energies

Hungerbühler, Norbert

In: Variational Problems in Riemannian Geometry, 2004, p. 45-64

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 p-energy. 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... More

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    Summary
    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 p-energy. 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 p-energy (p≠2) is much more difficult in many respects. We give a survey of the known results for the p-harmonic 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.