  We obtain Caccioppoli--type estimates for nontrivial and nonnegative
solutions to the anticoercive partial differential inequalities of elliptic
type involving degenerated $p$--Laplacian: $-\Delta_{p,a} u:=
-\mathrm{div}(a(x)|\na u|^{p-2}\na u)\ge b(x)\Phi (u)$, where $u$ is defined in
a domain $\Omega$. Using Caccioppoli--type estimates, we obtain several
variants of Hardy--type inequalities in weighted Sobolev spaces.
