Estimates of Heat Kernel of Fractional Laplacian Perturbed by Gradient Operators

Communications in Mathematical Physics volume 271, pages 179–198 (2007)Cite this article

Abstract

We construct a continuous transition density of the semigroup generated by \({\Delta^{\alpha/2} + b(x)\cdot \nabla}\) for \({1 < \alpha < 2, d\ge 1}\) and b in the Kato class \({\mathcal{K}_d^{\alpha-1}}\) on \({\mathbb{R}^d}\) . For small time the transition density is comparable with that of the fractional Laplacian.

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Affiliations

  1. Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Krzysztof Bogdan & Tomasz Jakubowski

Authors
  1. Krzysztof Bogdan
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  2. Tomasz Jakubowski
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Correspondence to Krzysztof Bogdan.

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Partially supported by KBN and MEN.

Communicated by B. Simon

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Bogdan, K., Jakubowski, T. Estimates of Heat Kernel of Fractional Laplacian Perturbed by Gradient Operators. Commun. Math. Phys. 271, 179–198 (2007). https://doi.org/10.1007/s00220-006-0178-y

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Keywords

  • Green Function
  • Heat Kernel
  • Lipschitz Domain
  • Transition Density
  • Pseudo Differential Operator