We derive continuous dependence estimates for weak entropy solutions of degenerate parabolic equations with nonlinear fractional diffusion. The diffusion term involves the fractional Laplace operator, ∆α/2 for α ∈ (0, 2). Our results are quantitative and we exhibit an example for which they are optimal. We cover the dependence on the nonlinearities, and for the first time, the Lipschitz depende...

In this article, we give an integral representation of the resolvent kernel on H-type groups, then derive Kaplan's fundamental solution groups. Also obtain Green for fractional powers its sub-Laplacian.

We provide a new characterization of homogeneous Besov and Sobolev spaces in Carnot groups using the fractional heat kernel Poisson kernel. apply our results to study commutators involving powers sub-Laplacian.