On quasielliptic operators in \(\mathbb{R}_n\) (Q1288113)

The author studies a class of matrix quasielliptic operators \(\mathcal L(D_x) =(l_{k,j}(D_x))\) defined on the whole \(\mathbb{R}_n\). For these operators, some isomorphy properties are established and unique solvability is proven for the systems \[ \mathcal L(D_x)U = F(x), \quad x\in \mathbb{R}_n, \] in special weighted Sobolev spaces. An application of the results to the theory of the equations which are not solved with respect to the higher order derivative is illustrated by an example.