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T:A:L:K:S
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title:
Heat kernel estimates for Dirichlet fractional Laplacian perturbed by gradient operators in C^{1,1} open sets |
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name:
Song |
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first name:
Renming
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location/conference:
levy10
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abstract:
\\name{Renming Song}
\\poster{Heat kernel estimates for Dirichlet fractional Laplacian
Perturbed by Gradient Operators in $C^{1,1}$ Open Sets}
Suppose that $\\alpha\\in (1, 2)$.
Consider the fractional Laplacian perturbed by
gradient operator $-(-\\Delta)^{\\alpha /2}+ b(x) \\cdot \\nabla$ on an
bounded $C^{1,1}$ open subset in ${\\mathb R}^d$ with zero exterior
condition. We will assume $b=(b1, \\cdots, b^d)$ is such
that each component $b^i$, $i=1, \\dots, d$ belongings to an appropriate
Kato class. In this talk, I will present sharp two-sided estimates for the
heat kernel of such operators.
\\textbf{References:}
\\begin{enumerate}
\\item Z.-Q. Chen, P. Kim and R. Song, Sharp density function
estimates for Feynman-Kac semigroups of stable processes in open
sets,
preprint, 2010.
\\item Z.-Q. Chen, P. Kim and R. Song, Heat kernel estimates for
Dirichlet fractional Laplacian
Perturbed by Gradient Operators in $C^{1,1}$ Open Sets, preprint, 2010.
\\end{enumerate}
\\hrulefill\\newline
\\address{Department of Mathematics, University of Illinois, Urbana, IL
61801, USA}
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