Heat Flow into Spheres for a Class of Energies

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


Let M and N be compact smooth Riemannian manifolds without boundaries. Then, for a map u: MN, 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.


Heat Flow Weak Solution Homotopy Class Energy Inequality Young Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Basel AG 2004

Authors and Affiliations

  • Norbert Hungerbühler
    • 1
  1. 1.Department of MathematicsUniversity of Fribourg, PérollesFribourgSwitzerland

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