Liouville-type theorems for nonlinear degenerate parabolic equation

We study Liouville-type theorems for degenerate parabolic equation of the form where and . We prove the optimal Liouville-type results in dimension , and for radial solutions in any dimension. We also provide some partial results for non-radial solutions in dimension . Our proofs are based on a generalized Gidas-Spruck technique, combined with the idea of Serrin and Zou (Acta Math 189(1):79-142, 2002) and of Bidaut-V,ron (Aequations aux d,riv,es partielles et applications. Elsevier, Paris, pp 189-198, 1998). Finally, we clarify and correct some of the previous results on this topic.