Existence in nonlocal elasticity

The displacement boundary value problems of homogeneous, isotropic, linear, nonlocal elasticity are defined. A Hilbert space is defined and an inequality which plays an important role in the existence theory of elasticity is proven. Finally, it is shown that the bilinear form which appears in the weak formulation satisfies the requirements of the fundamental existence lemma (Lax-Milgram's Theorem)