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Global heat kernel estimates for $\Delta+\Delta^{\alpha/2}$ in half-space-like domains

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Global heat kernel estimates for $\Delta+\Delta^{\alpha/2}$ in half-space-like domains
2.	Creator	Author's name, affiliation, country	Zhen-Qing Chen; University of Washington; United States
2.	Creator	Author's name, affiliation, country	Panki Kim; Seoul National University; Korea, Republic Of
2.	Creator	Author's name, affiliation, country	Renming Song; University of Illinois at Urbana-Champaign; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	symmetric $\alpha$-stable process, heat kernel, transition density, Green function, exit time, L\'evy system, harmonic function, fractional Laplacian, Laplacian, Brownian motion
3.	Subject	Subject classification	Primary 60J35, 47G20, 60J75; Secondary 47D07
4.	Description	Abstract	Suppose that $d\ge 1$ and $\alpha\in (0, 2)$. In this paper, we establish by using probabilistic methods sharp two-sided pointwise estimates for the Dirichlet heat kernels of $\{\Delta+ a^\alpha \Delta^{\alpha/2}; \ a\in (0, 1]\}$ on half-space-like $C^{1, 1}$ domains for all time $t>0$. The large time estimates for half-space-like domains are very different from those for bounded domains. Our estimates are uniform in $a \in (0, 1]$ in the sense that the constants in the estimates are independent of $a\in (0, 1]$. Thus they yield the Dirichlet heat kernel estimates for Brownian motion in half-space-like domains by taking $a\to 0$. Integrating the heat kernel estimates with respect to the time variable $t$, we obtain uniform sharp two-sided estimates for the Green functions of $\{\Delta+ a^\alpha \Delta^{\alpha/2}; \ a\in (0, 1]\}$ in half-space-like $C^{1, 1}$ domains in $R^d$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	NSF, NRF and the Simons Foundation
7.	Date	(YYYY-MM-DD)	2012-04-25
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/1751
10.	Identifier	Digital Object Identifier	10.1214/EJP.v17-1751
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 17
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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