On the nonexistence of solutions of some anisotropic elliptic and backward parabolic inequalities (Q268021)

The paper under review deals with higher-order elliptic and parabolic inequalities of the form \[ \sum_{i=1}^N \sum_{\ell_i\leq\alpha_i\leq m_i} D_{x_i}^{\alpha_i}(A_{\alpha_i}(x,u))\geq f(x,u)\quad x\in \mathbb{R}^N, \] and \[ u_t+\sum_{i=1}^N \sum_{k_i\leq\beta_i\leq n_i} D_{x_i}^{\beta_i}(B_{\beta_i}(x,t,u))\geq g(x,t,u)\quad (x,t)\in \mathbb{R}^N\times \mathbb{R}_+, \] where \(\ell_i,m_i,k_i,n_i\in\mathbb{N},\) \(\ell_i,k_i>1,\) and \(A_{\alpha_i},\) \(B_{\beta_i},\) \(f\) and \(g\) are given Carathéodory functions. Under appropriate conditions on the coefficients and the right-hand sides, regarding mainly their growths with respect to \(u\), the author proves nonexistence of weak solutions to the above differential inequalities.