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The present article is an overview of some mathematical results, which
provide elements of rigorous basis for some multiscale
computations in materials science. The emphasis is laid upon atomistic
to continuum limits for crystalline materials. Various mathematical
approaches are addressed. The
setting is stationary. The relation to existing techniques used in the engineering
literature is investigated.
We prove existence and uniqueness results for the solution of nonlinear elliptic boundary value problems, where the linear part of the equation is given by a second-order elliptic operator not in divergence form.
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