标题： 关于原子论和连续介质非线性弹性理论中边值问题解的存在性和收敛性 显示英文标题

标题： Existence and Convergence of Solutions of the Boundary Value Problem in Atomistic and Continuum Nonlinear Elasticity Theory

摘要： 我们证明了在有界区域上，静止的原子非线性弹性力学方程解的存在性，并且给定了边界值。我们还展示了这些解如何在相邻原子间距趋于零时收敛于连续介质非线性弹性力学理论的解，其中能量密度由Cauchy-Born规则给出。这些结果对于一般的有限范围相互作用势，在靠近稳定晶格的小数据附近成立。我们还详细讨论了稳定性概念。 显示英文摘要

摘要： We show existence of solutions for the equations of static atomistic nonlinear elasticity theory on a bounded domain with prescribed boundary values. We also show their convergence to the solutions of continuum nonlinear elasticity theory, with energy density given by the Cauchy-Born rule, as the interatomic distances tend to zero. These results hold for small data close to a stable lattice for general finite range interaction potentials. We also discuss the notion of stability in detail.