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Heat Flow into Spheres for a Class of Energies

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Variational Problems in Riemannian Geometry

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 59))

Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Fribourg, Pérolles, Fribourg, CH-1700, Switzerland

    Norbert Hungerbühler

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  1. Norbert Hungerbühler
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Editors and Affiliations

  1. Département de Mathématiques, Université de Bretagne Occidentale, UFR Science et Technique 6, avenue Victor Le Gorgeu, B.P. 809, Brest Cedex, 29285, France

    Paul Baird , Ali Fardoun  & Rachid Regbaoui ,  & 

  2. Laboratoire de Mathématiques et Physique Théorique, UMR 6083 du CNRS Université de Tours, Parc de Grandmont, Tours Cedex, 37200, France

    Ahmad El Soufi

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Hungerbühler, N. (2004). Heat Flow into Spheres for a Class of Energies. In: Baird, P., Fardoun, A., Regbaoui, R., El Soufi, A. (eds) Variational Problems in Riemannian Geometry. Progress in Nonlinear Differential Equations and Their Applications, vol 59. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7968-2_4

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  • DOI: https://doi.org/10.1007/978-3-0348-7968-2_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9640-5

  • Online ISBN: 978-3-0348-7968-2

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