On weak solutions of boundary value problems within the surface elasticity of <i>N</i> th order

A study of existence and uniqueness weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the strain energy as a quadratic function tensor deformation gradients up Nth order. virtual work principle, extended for higher-order gradient media, serves basis defining solution. In order characterize smoothness such solutions, certain functional spaces Sobolev type are introduced. Compared obtained in classical linear elasticity, solids stresses smoother on boundary; more precisely, solution belongs H 1 ( V ) ? N S s where ? ? ? R 3 .