대한수학회지 (Journal of the Korean Mathematical Society)

  • 제56권1호
  • /
  • Pages.91-111
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  • 2019
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  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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HEAT KERNEL ESTIMATES FOR DIRICHLET FRACTIONAL LAPLACIAN WITH GRADIENT PERTURBATION

  • Chen, Peng (Department of Mathematics University of Macau) ;
  • Song, Renming (Department of Mathematics University of Illinois) ;
  • Xie, Longjie (School of Mathematics and Statistics Jiangsu Normal University) ;
  • Xie, Yingchao (School of Mathematics and Statistics Jiangsu Normal University)
  • 투고 : 2018.01.30
  • 심사 : 2018.06.26
  • 발행 : 2019.01.01
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초록

We give a direct proof of the sharp two-sided estimates, recently established in [4, 9], for the Dirichlet heat kernel of the fractional Laplacian with gradient perturbation in $C^{1,1}$ open sets by using Duhamel's formula. We also obtain a gradient estimate for the Dirichlet heat kernel. Our assumption on the open set is slightly weaker in that we only require D to be $C^{1,{\theta}}$ for some ${\theta}{\in}({\alpha}/2,1]$.

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참고문헌

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