Energy identity for intrinsically biharmonic maps in four dimensions
Energy identity for intrinsically biharmonic maps in four dimensions
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DOI：
10.2140/apde.2012.5.61
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发表时间：
2012-06
期刊：
影响因子：
2.2
通讯作者：
Peter Hornung;R. Moser
中科院分区：
文献类型：
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作者：
Peter Hornung;R. Moser
设u是从有界域S_n ~ 4到紧黎曼流形N的映射。它的内禀双调和能量E2.u由u的内禀海森的平方L2范数给出。我们考虑E2的临界点的弱收敛序列。我们的主要结果是，能量耗散沿着这样的序列是完全由于能量集中在一个有限的集合，并耗散的能量等于超过E1的许多整个临界点的能量的总和。
Let u be a mapping from a bounded domain S ⊂ ℝ4 into a compact Riemannian manifold N. Its intrinsic biharmonic energy E2.u/ is given by the squared L2-norm of the intrinsic Hessian of u. We consider weakly converging sequences of critical points of E2. Our main result is that the energy dissipation along such a sequence is fully due to energy concentration on a finite set and that the dissipated energy equals a sum over the energies of finitely many entire critical points of E1.