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تسجيل مستخدم جديدHeat kernel estimates for Dirichlet fractional Laplacian with gradient perturbation
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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 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 $thetain (alpha/2, 1]$.
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