Minimizers of nonlocal polyconvex energies in nonlocal hyperelasticity

Abstract We develop a theory of existence minimizers energy functionals in vectorial problems based on nonlocal gradient under Dirichlet boundary conditions. The model shares many features with the peridynamics and is also applicable to solid mechanics, especially nonlinear elasticity. This was introduced an earlier work, inspired by Riesz’ fractional gradient, but suitable for bounded domains. main assumption integrand polyconvexity. Thus, we adapt corresponding results classical case this context, notably, Piola’s identity, integration parts determinant weak continuity determinant. proof exploits fact that every gradient.