HEAT KERNEL ESTIMATES FOR THE FRACTIONAL LAPLACIAN WITH DIRICHLET CONDITIONS

被引：98

作者：

Bogdan, Krzysztof ^{[1
]}

Grzywny, Tomasz ^{[1
]}

Ryznar, Michal ^{[1
]}

机构：

[1] Wroclaw Univ Technol, Inst Math & Comp Sci, PL-50370 Wroclaw, Poland

来源：

ANNALS OF PROBABILITY | 2010年 / 38卷 / 05期

关键词：

Fractional Laplacian; Dirichlet problem; heat kernel estimate; Lipschitz domain; boundary Harnack principle; SYMMETRIC STABLE PROCESSES; GREEN-FUNCTIONS; LIPSCHITZ-DOMAINS; INTRINSIC ULTRACONTRACTIVITY; SCHRODINGER OPERATOR; HARNACK INEQUALITY; HARMONIC FUNCTIONS; JUMP-PROCESSES; SPACES; PERTURBATIONS;

D O I：

10.1214/10-AOP532

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet condition for a general class of domains including Lipschitz domains.

引用

页码：1901 / 1923

页数：23

共 44 条

[1]

[Anonymous], 1999, CAMBRIDGE STUD ADV M

[2]

[Anonymous], 2006, Hiroshima Math. J.

[3] Symmetric stable processes in cones [J].

Bañuelos, R ;

Bogdan, K .

POTENTIAL ANALYSIS, 2004, 21 (03) :263-288

[4] Trace estimates for stable processes [J].

Banuelos, Rodrigo ;

Kulczycki, Tadeusz .

PROBABILITY THEORY AND RELATED FIELDS, 2008, 142 (3-4) :313-338

[5] Heat kernel upper bounds for jump processes and the first exit time [J].

Barlow, Martin T. ;

Grigor'yan, Alexander ;

Kumagai, Takashi .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2009, 626 :135-157

[6]

Blumenthal R. M., 1960, Trans. Amer. Math. Soc, V95, P263, DOI [DOI 10.1090/S0002-9947-1960-0119247-6, 10.1090/S0002-9947-1960-0119247-6]

[7]

Blumenthal R.M., 1961, Transactions of the American Mathematical Society, V99, P540, DOI [10.2307/1993561, DOI 10.2307/1993561]

[8] On Kelvin transformation [J].

Bogdan, K. ;

Zak, T. .

JOURNAL OF THEORETICAL PROBABILITY, 2006, 19 (01) :89-120

[9]

Bogdan K, 1999, STUD MATH, V133, P53

[10] Sharp estimates for the Green function in Lipschitz domains [J].

Bogdan, K .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 243 (02) :326-337

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