Radial Symmetry of p-Harmonic Minimizers
Radial Symmetry of p-Harmonic Minimizers
复制标题
DOI：
10.1007/s00205-018-1246-0
复制
发表时间：
2017-10
影响因子：
2.5
通讯作者：
Aleksis Koski;Jani Onninen
中科院分区：
文献类型：
--
作者：
Aleksis Koski;Jani Onninen
“仍然不知道 Ball（Philos Trans R Soc Lond A 306:557–611, 1982）（以及随后许多其他人）获得的径向空化最小化器是否是任何物理上合理的非线性弹性能量的全局最小化器”。这段引文来自SivaloganathanandSpector(Ann Inst Henri Poincaré Anal Non Linéaire 25(1):201–213, 2008)，似乎仍然准确。这里考虑 p 谐波能量的模型情况。我们证明，只要我们规定了边界上的允许变形，平面径向最小化器确实是全局最小化器。然而，在无牵引设置中，即使恒等映射也不需要是全局最小化器。
“It is still not known if the radial cavitating minimizers obtained byBall(Philos Trans R Soc Lond A 306:557–611, 1982) (and subsequently by many others) are global minimizers of any physically reasonable nonlinearly elastic energy”. This quotation is fromSivaloganathanandSpector(Ann Inst Henri Poincaré Anal Non Linéaire 25(1):201–213, 2008) and seems to be still accurate. The model case of thep-harmonic energy is considered here. We prove that the planar radial minimizers are indeed the global minimizers provided we prescribe the admissible deformations on the boundary. In the traction free setting, however, even the identity map need not be a global minimizer.