Hölder Estimates for Nonlocal-Diffusion Equations with Drifts

Zhen-Qing Chen; Xicheng Zhang

doi:10.1007/s40304-015-0042-5

Communications in Mathematics and Statistics ›› 2014, Vol. 2 ›› Issue (3-4) : 331 -348. DOI: 10.1007/s40304-015-0042-5

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Hölder Estimates for Nonlocal-Diffusion Equations with Drifts

Zhen-Qing Chen ¹^,^a
, Xicheng Zhang ²

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Abstract

We study a class of nonlocal-diffusion equations with drifts, and derive a priori $\Phi $-Hölder estimate for the solutions by using a purely probabilistic argument, where $\Phi $ is an intrinsic scaling function for the equation.

Keywords

Parabolic function / Hölder regularity / Nonlocal operator / Drift / Space-time Hunt process / Lévy system

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Zhen-Qing Chen, Xicheng Zhang. Hölder Estimates for Nonlocal-Diffusion Equations with Drifts. Communications in Mathematics and Statistics, 2014, 2(3-4): 331-348 DOI:10.1007/s40304-015-0042-5

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