We consider the fractional porous medium flow introduced by Caffarelli and Vazquez (2011) obtain local in time existence, uniqueness, blow-up criterion for smooth solutions. The proof is based on establishing a commutator estimate involving Laplacian operators.

We consider stochastic flow on Rn driven by fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1), and study tangent flow and the growth of the Hausdorff measure of sub-manifolds of Rn as they evolve under the flow. The main result is a bound on the rate of (global) growth in terms of the (local) Hölder norm of the flow.

We consider stochastic flow on Rn driven by fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1), and study tangent flow and the growth of the Hausdorff measure of sub-manifolds of Rn as they evolve under the flow. The main result is a bound on the rate of (global) growth in terms of the (local) Hölder norm of the flow.

Abstract We consider the fractional mean curvature flow of entire Lipschitz graphs. provide regularity results, and we study long time asymptotics flow. In particular show that in a suitable rescaled framework, if initial graph is sublinear perturbation cone, evolution asymptotically approaches an expanding self-similar solution. also prove stability hyperplanes convex cones unrescaled setting.

1. A study has been undertaken in six healthy male subjects to clarify whether post-proximal segments of the nephron contribute to the renal handling of lithium under conditions of maximal forced osmotic load diuresis and arginine vasopressin-induced antidiuresis. Increments in the fractional clearance of free water, as a measure of effect at the proximal tubule, were positively correlated with...