Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradient

Longjie Xie; Renming Song; Yingchao Xie

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Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradient

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arxiv 1712.07565 v1 pith:U3QAPQPI submitted 2017-12-20 math.PR math.AP

Renming Song , Longjie Xie , Yingchao Xie This is my paper · ORCID

classification math.PRmath.AP

keywords gradientheatkernelestimatesfractionallaplaciansharpspectral

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abstract

By using Duhamel's formula, we prove sharp two-sided estimates for the heat kernel of spectral fractional Laplacian with time-dependent gradient perturbation in bounded $C^{1,1}$ domains. Moreover, we also obtain gradient estimate as well as H\"older continuity of the gradient of the heat kernel.

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