Holder estimates for advection fractional-diffusion equations
By Luis Silvestre. 2010
106 citations recorded by the source corpus.
We analyse conditions for an evolution equation with a drift and fractional diffusion to have a Holder continuous solution. In case the diffusion is of order one or more, we obtain Holder estimates for the solution for any bounded drift. In the case when the diffusion is of order less than one, we require the drift to be a Holder continuous vector field in order to obtain the same type of regularity result.
View Paper: https://www.semanticscholar.org/paper/85bf90623e2df16700854f94abe5f3ad5a1105e8
How researchers see this paper
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- Lorenzo Brasco
- Russell W. Schwab
- Erik Lindgren
- Roman Shvydkoy
- Thomas Alazard
- Quoc-Hung Nguyen
- Martin H. Strömqvist
- Luis Silvestre
Citations in the corpus
- Continuity of solutions to a nonlinear fractional diffusion equation (2019, background): “We mention only a fraction of it, namely [7, 22, 23, 29, 30] and [32].”
- Endpoint Sobolev Theory for the Muskat Equation (2020, methodology): “In the critical case α = 1, the global in time well-posedness has been proved by Kiselev-Nazarov-Volberg [39], CaffarelliVasseur [13] and Constantin-Vicol [27] (see also [38, 49, 54, 45]).”
- On the Loss of Continuity for Super-Critical Drift-Diffusion Equations (2012, background): “Using the ideas from [33], the result was generalized to non divergence-free drifts in [32].”
- Eulerian dynamics with a commutator forcing III. Fractional diffusion of order 0 (2017, result): “[13] R. W. Schwab and L. Silvestre.”
- Traveling wave solutions of Allen–Cahn equation with a fractional Laplacian (2015, background): “By the regularity theory for fractional Laplacians (see [13,47,63,64,82] and [83]), for any 0 < α < 1, there exists some constant C > 0 which just depends on s, G0 and G1 such that ‖uk‖C2,α(Rn) ≤ C, ∀k ≥ 1.”
- Regularity for parabolic integro-differential equations with very irregular kernels (2014, methodology): “Also, it might be possible to extend our regularity results for equations with Hölder continuous drifts and α < 1 as in [37], although we do point out that the technique from [37] does not work right away with the methods in this paper.”