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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Communicated by B. Simon
Partially supported by KBN and MEN.
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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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DOI: https://doi.org/10.1007/s00220-006-0178-y