Liouville theorem for second order elliptic equation with degenerating coefficients (Q1406367)

The author studies the homogeneous elliptic equation \[ \sum\limits_{i,\,j=1}^n a_{ij}(x)\, \frac{\partial^2u}{\partial x_i\partial x_j} = 0 \] in the Euclidean space \(\mathbb R^n\). It is assumed the coefficients can degenerate uniformly in \(| x| \) as \(\,| x| \to\infty\). He establishes the relationship between the degenerate velocity of the coefficients \(a_{ij}(x)\) and the minimal growth velocity of the nontrivial classical solution of the given equation.