Heat kernel of fractional Laplacian in cones
نویسندگان
چکیده
منابع مشابه
Heat Kernel Estimates for Dirichlet Fractional Laplacian
In this paper, we consider the fractional Laplacian −(−∆)α/2 on an open subset in R with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such Dirichlet fractional Laplacian in C open sets. This heat kernel is also the transition density of a rotationally symmetric α-stable process killed upon leaving a C open set. Our results are the first sharp two-sided ...
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Explicit sharp estimates for the Green function of the Laplacian in C domains were completed in 1986 by Zhao [42]. Sharp estimates of the Green function of Lipschitz domains were given in 2000 by Bogdan [6]. Explicit qualitatively sharp estimates for the classical heat kernel in C domains were established in 2002 by Zhang [41]. Qualitatively sharp heat kernel estimates in Lipschitz domains were...
متن کاملDirichlet Heat Kernel Estimates for Fractional Laplacian with Gradient Perturbation
By Zhen-Qing Chen∗,‡, Panki Kim†,§ and Renming Song¶ University of Washington‡, Seoul National University§ and University of Illinois¶ Suppose that d ≥ 2 and α ∈ (1, 2). Let D be a bounded C open set in R and b an R-valued function on R whose components are in a certain Kato class of the rotationally symmetric α-stable process. In this paper, we derive sharp two-sided heat kernel estimates for ...
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Abstract. We consider the fractional Laplacian −(−1)α/2 on an open subset in Rd with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such a Dirichlet fractional Laplacian inC1,1 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 twoside...
متن کاملDirichlet Heat Kernel Estimates for Fractional Laplacian with Gradient Perturbation by Zhen-qing Chen1,
Since 1 < α < 2, using Hölder’s inequality, it is easy to see that for every p > d/(α − 1), L∞(Rd;dx) + Lp(Rd;dx) ⊂ Kd,α−1. Throughout this paper we will assume that b = (b1, . . . , b) is an R -valued function on R such that |b| ∈ Kd,α−1. Define L = α/2 + b · ∇ . Intuitively, the fundamental solution p(t, x, y) of L and the fundamental solution p(t, x, y) of α/2, which is also the transition d...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 2010
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm118-2-1