Heat kernel estimates for time fractional equations
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 ...
متن کاملHeat kernel estimates for the fractional Laplacian
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 کاملStrichartz Type Estimates for Fractional Heat Equations
We obtain Strichartz estimates for the fractional heat equations by using both the abstract Strichartz estimates of Keel-Tao and the HardyLittlewood-Sobolev inequality. We also prove an endpoint homogeneous Strichartz estimate via replacing L∞x (R ) by BMOx(R) and a parabolic homogeneous Strichartz estimate. Meanwhile, we generalize the Strichartz estimates by replacing the Lebesgue spaces with...
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 ...
متن کاملHeat kernel estimates for the Dirichlet fractional Laplacian
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...
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ژورنال
عنوان ژورنال: Forum Mathematicum
سال: 2018
ISSN: 1435-5337,0933-7741
DOI: 10.1515/forum-2017-0192