Hölder Estimates for Nonlocal-Diffusion Equations with Drifts

Zhen Qing Chen; Xicheng Zhang

doi:10.1007/s40304-015-0042-5

Hölder Estimates for Nonlocal-Diffusion Equations with Drifts

Zhen Qing Chen^*, Xicheng Zhang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	331-348
Number of pages	18
Journal	Communications in Mathematics and Statistics
Volume	2
Issue number	3-4
DOIs	https://doi.org/10.1007/s40304-015-0042-5
Publication status	Published - 1 Dec 2014
Externally published	Yes

Keywords

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

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10.1007/s40304-015-0042-5

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Chen, Z. Q., & Zhang, X. (2014). Hölder Estimates for Nonlocal-Diffusion Equations with Drifts. Communications in Mathematics and Statistics, 2(3-4), 331-348. https://doi.org/10.1007/s40304-015-0042-5

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abstract = "We study a class of nonlocal-diffusion equations with drifts, and derive a priori Φ -H{\"o}lder estimate for the solutions by using a purely probabilistic argument, where Φ is an intrinsic scaling function for the equation.",

keywords = "Drift, H{\"o}lder regularity, L{\'e}vy system, Nonlocal operator, Parabolic function, Space-time Hunt process",

author = "Chen, {Zhen Qing} and Xicheng Zhang",

note = "Publisher Copyright: {\textcopyright} 2015, School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag Berlin Heidelberg.",

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AU - Zhang, Xicheng

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

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KW - Hölder regularity

KW - Lévy system

KW - Nonlocal operator

KW - Parabolic function

KW - Space-time Hunt process

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Hölder Estimates for Nonlocal-Diffusion Equations with Drifts

Abstract

Keywords

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