Liouville’s type results for singular anisotropic operators.

We present two Liouville-type results for solutions to anisotropic elliptic equations that have a growth of power 2 along the first s coordinate directions and of power p, with 1 < p < 2 along the other (N − s) ones. First, we begin our investigation by assuming that the solution is bounded only from below, deriving a rigidity result for the range p + (N − s)(p − 2) > 0 of non-degeneration, which is a purely parabolic shade. Then we break free from this constraint at the price of assuming the solution to be bounded also from above. In honor of Professor Ermanno Lanconelli, on the occasion of his 80th birthday