Existence and nonexistence results for higher order evolution inequalities posed outside the half-ball (Q6612850)

This article is concerned with qualitative properties of solutions to the higher order evolution inequality \(\partial_t^k u-\Delta u+\frac{\lambda}{|x|^2}u\geq |x|^\tau |u|^p\) in \(\Omega\). Here \(\Omega=\{x\in \mathbb{R}^N, |x|>1, x_N>0\}\), \(\tau\in \mathbb{R}\), \(p>1\). There are two main results which establish the various conditions on the exponents for the existence and nonexistence of solutions in the weak sense. Comparisons with the stationary case are also discussed in the article, as well as cases in which the conditions obtained by the authors become optimal. The approach relies on various integral estimates.