Keller-Osserman a priori estimates and the Harnack inequality for the evolution \(p\)-Laplace equation with singular absorption term
In this paper, the author studies quasilinear equations of type \[ u_t-\operatorname{div}(|\nabla u| ^{p-2}\nabla u)+V(x)f(u)=0, \] where \(p\geq 2\) and \(u \geq 0\). Starting from the original ideas due to DiBenedetto-Gianazza-Vespri, many authors proved intrinsic Harnack estimates for evolution \(p\)-Laplace type equations with lower order terms from Kato classes and with absorption term. In this paper, the author makes a first attempt to study the Harnack inequality for degenerate quasilinear parabolic equations perturbed by singular absorption term. Despite the lack of comparison principle, he proves a priori estimates of Keller-Osserman type, and using these estimates he shows that a suitable intrinsic Harnack inequality holds.
scientific article; zbMATH DE number 6925394
scientific article