Existence and Convergence of Solutions of the Boundary Value Problem in Atomistic and Continuum Nonlinear Elasticity Theory
Analysis of PDEs
2016-06-30 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1604.00197,
title = {Existence and Convergence of Solutions of the Boundary Value Problem in Atomistic and Continuum Nonlinear Elasticity Theory},
author = {Julian Braun and Bernd Schmidt},
journal= {arXiv preprint arXiv:1604.00197},
year = {2016}
}
Comments
new version with only minor changes