A hyperbolic polyharmonic system in an exterior domain - Manal Alfulaij; Mohamed Jleli; Bessem Samet (AIMS Mathematics)
A nonlinear hyperbolic polyharmonic system in an exterior domain of $ \mathbb{R}^N $ is considered under inhomogeneous Navier-type boundary conditions. Using nonlinear capacity estimates specifically adapted to the polyharmonic operator $ (-Δ)^m $, the geometry of the domain, and the boundary conditions, a sharp criterium for the nonexistence of weak solutions is obtained. Next, an optimal nonexistence result for the corresponding stationary problem is deduced.