论文标题
在2D中存在SDRI模型的最小化器：与不匹配菌株的润湿和脱水状态
Existence of minimizers for the SDRI model in 2d: wetting and dewetting regime with mismatch strain
论文作者
论文摘要
[Kholmatov-Piovano 2020]中引入的模型在应力驱动重排稳定性的框架中[SDRI）[Asaro-Tiller 1972;格林菲尔德（Grinfeld）1993}对于压力下的结晶材料的形态。如[Kholmatov-Piovano 2020]中，并且与[Lowengrub等人的模型一致。 2009; Spencer 1999]是一种不匹配的菌株，而不是[Crismale-Friedrich 2020]中的Dirichlet条件，被认为包括在分析中，晶体和可能的相邻（支撑）材料之间的晶格不匹配。在不存在类似图的假设的情况下，以二维形式建立了溶液的存在，并限制了有限数量的$ m $连接组件，用于由结晶材料占据的区域的自由边界，从而扩展了表面上施加的薄膜和材料腔的先前结果。 Due to the lack of compactness and lower semicontinuity for the sequences of $m$-minimizers, i.e., minimizers among configurations with at most $m$ connected boundary components, a minimizing candidate is directly constructed, and then shown to be a minimizer by means of uniform density estimates and the convergence of $m$-minimizers' energies to the energy infimum as $ m \至\ infty $。最后，建立了每个最小化器满足形态的规则性能。
The model introduced in [Kholmatov-Piovano 2020] in the framework of the theory on Stress-Driven Rearrangement Instabilities (SDRI) [Asaro-Tiller 1972; Grinfeld 1993} for the morphology of crystalline materials under stress is considered. As in [Kholmatov-Piovano 2020] and in agreement with the models in [Lowengrub et al. 2009; Spencer 1999], a mismatch strain, rather than a Dirichlet condition as in [Crismale-Friedrich 2020], is considered to include into the analysis the lattice mismatch between the crystal and possible adjacent (supporting) materials. The existence of solutions is established in dimension two in the absence of graph-like assumptions and of the restriction to a finite number $m$ of connected components for the free boundary of the region occupied by the crystalline material, thus extending previous results for epitaxially strained thin films and material cavities. Due to the lack of compactness and lower semicontinuity for the sequences of $m$-minimizers, i.e., minimizers among configurations with at most $m$ connected boundary components, a minimizing candidate is directly constructed, and then shown to be a minimizer by means of uniform density estimates and the convergence of $m$-minimizers' energies to the energy infimum as $m\to\infty$. Finally, regularity properties for the morphology satisfied by every minimizer are established.
