A Perturbed Cauchy Viscoelastic Problem in an Exterior Domain

Abstract

A Cauchy viscoelastic problem perturbed by an inverse-square potential, and posed in an exterior domain of R^N, is considered under a Dirichlet boundary condition. Using nonlinear capacity estimates specifically adapted to the non-local nature of the problem, the potential function and the boundary condition, we establish sufficient conditions for the nonexistence of weak solutions.