q-moment estimates for the singular p-Laplace equation and applications

We provide q-moment estimates on annuli for weak solutions of the singular p-Laplace equation where p and q are conjugates. We derive q-uniform integrability for some critical parameter range. As applications, we derive a mass conservation as well as a weak convergence result for a larger critical parameter range. Concerning the latter point, we further provide a rate of convergence of order tq−1 of the solution in the q-Wasserstein distance.