Analysis of an atomistic model for anti-plane fracture

@article{Buze2018AnalysisOA,
  title={Analysis of an atomistic model for anti-plane fracture},
  author={Maciej Buze and T. Hudson and C. Ortner},
  journal={arXiv: Analysis of PDEs},
  year={2018}
}
We develop a model for an anti-plane crack defect posed on a square lattice under an interatomic pair-potential with nearest-neighbour interactions. In particular, we establish existence, local uniqueness and stability of solutions for small loading parameters and further prove qualitatively sharp far-field decay estimates. The latter requires establishing decay estimates for the corresponding lattice Green's function, which are of independent interest. 
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