Geodesic
Heat kernel estimates for the Dirichlet fractional Laplacian
Journal of the European Mathematical Society, Tome 12 (2010) no. 5, pp. 1307-1329 Cet article a éte moissonné depuis la source EMS Press

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In this paper, we consider the fractional Laplacian −(−Δ)α/2 on an open subset in Rd with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such Dirichlet fractional Laplacian in C1,1 open sets. This heat kernel is also the transition density of a rotationally symmetric α-stable process killed upon leaving a C1,1 open set. Our results are the first sharp two-sided estimates for the Dirichlet heat kernel of a non-local operator on open sets.
DOI : 10.4171/jems/231
Classification : 60-XX, 47-XX, 00-XX
Keywords: Fractional Laplacian, symmetric α-stable process, heat kernel, transition density, Green function, exit time, Lévy system, boundary Harnack inequality, parabolic Harnack inequality, intrinsic ultracontractivity 
@article{JEMS_2010_12_5_a8,
     author = {Zhen-Qing Chen and Panki Kim and Renming Song},
     title = {Heat kernel estimates for the {Dirichlet} fractional {Laplacian}},
     journal = {Journal of the European Mathematical Society},
     pages = {1307--1329},
     year = {2010},
     volume = {12},
     number = {5},
     doi = {10.4171/jems/231},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/231/}
}
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Zhen-Qing Chen; Panki Kim; Renming Song. Heat kernel estimates for the Dirichlet fractional Laplacian. Journal of the European Mathematical Society, Tome 12 (2010) no. 5, pp. 1307-1329. doi: 10.4171/jems/231

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