Equilibrium Configurations of Epitaxially Strained Elastic Films: Second Order Minimality Conditions and Qualitative Properties of Solutions
Equilibrium Configurations of Epitaxially Strained Elastic Films: Second Order Minimality Conditions and Qualitative Properties of Solutions
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外延应变弹性薄膜的平衡构型：二阶极小值条件和解的定性性质
DOI：
10.1007/s00205-011-0451-x
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发表时间：
2012
影响因子：
2.5
通讯作者：
M. Morini
中科院分区：
文献类型：
--
作者：
N. Fusco;M. Morini
我们考虑物理文献中引入的变分模型，用于描述当两种材料之间存在晶格失配时，弹性薄膜在厚平坦基板上的外延生长。我们研究平衡配置的定量和定性特性，即自由能泛函的局部和全局最小化器。更准确地说，我们通过分析确定了平面结构局部极小性的临界阈值，并且我们还证明了有关其全局极小性的几个结果。还解决了非平坦全局最小化器中不出现奇点的问题。该论文的主要成果之一是局部极小性的新充分条件，它首次将基于第二变体的正性的经典准则扩展到具有体能和表面能的泛函的背景。
We consider a variational model introduced in the physical literature to describe the epitaxial growth of an elastic film over a thick flat substrate when a lattice mismatch between the two materials is present. We study quantitative and qualitative properties of equilibrium configurations, that is, of local and global minimizers of the free-energy functional. More precisely, we determine analytically the critical threshold for the local minimality of the flat configuration and we also prove several results concerning its global minimality. The non-occurrence of singularities in non-flat global minimizers is also addressed. One of the main results of the paper is a new sufficient condition for local minimality, which provides the first extension of the classical criteria based on the positivity of the second variation to the context of functionals with bulk and surface energies.