Heat Flow into Spheres for a Class of Energies
Heat Flow into Spheres for a Class of Energies
复制标题
热流进入一类能量的球体
DOI：
10.1007/978-3-0348-7968-2_4
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发表时间：
2004
影响因子：
1.2
通讯作者：
N. Hungerbühler
中科院分区：
文献类型：
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作者：
N. Hungerbühler
令 M 和 N 为无边界紧致光滑黎曼流形。然后，对于映射 u: M → N，我们考虑一类能量，其中包括流行的狄利克雷能量和更一般的 p 能量。几何或物理问题促使人们研究这种能量的临界点或相应的热流问题。就狄利克雷能量而言，热流问题已得到深入研究并现已得到很好的理解。然而，事实证明，p 能量（p ≠ 2）的情况在许多方面要困难得多。我们对 p 谐波流的已知结果进行了调查，并指出如何通过使用最近针对拟线性问题开发的杨氏测量技术将这些结果扩展到更大类别的能量类型。
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.