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• W2963248977 abstract "For $dgeq1$ and $0<beta<alpha<2$, consider a family of pseudo differential operators ${Delta^{alpha} + a^beta Delta^{beta/2}$; $a in[0, 1]}$ on $mathbb{R}^d$ that evolves continuously from $Delta^{alpha/2}$ to $ Delta^{alpha/2}+ Delta^{beta/2}$. It gives arise to a family of Lévy processes ${X^a, ain[0, 1]}$ on $mathbb{R}^d$, where each $X^a$ is the independent sum of a symmetric $alpha$-stable process and a symmetric $beta$-stable process with weight $a$. For any $C^{1,1}$ open set $Dsubsetmathbb{R}^d$, we establish explicit sharp two-sided estimates, which are uniform in $ain(0, 1]$, for the transition density function of the subprocess $X^{a, D}$ of $X^a$ killed upon leaving the open set~$D$. The infinitesimal generator of $X^{a, D}$ is the nonlocal operator $Delta^{alpha} + a^betaDelta^{beta/2}$ with zero exterior condition on $D^c$. As consequences of these sharp heat kernel estimates, we obtain uniform sharp Green function estimates for $X^{a, D}$ and uniform boundary Harnack principle for $X^a$ in $D$ with explicit decay rate." @default.
• W2963248977 created "2019-07-30" @default.
• W2963248977 creator A5001365052 @default.
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• W2963248977 date "2010-01-01" @default.
• W2963248977 modified "2023-10-11" @default.
• W2963248977 title "Dirichlet heat kernel estimates for $Delta^{alpha/2}+ Delta^{beta/2}$" @default.
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• W2963248977 doi "https://doi.org/10.1215/ijm/1348505533" @default.
• W2963248977 hasPublicationYear "2010" @default.
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