Results 21 to 30 of about 403 (112)

Heat kernel estimates for the Dirichlet fractional Laplacian

Journal of the European Mathematical Society, 2010
In this paper, we consider the fractional Laplacian -(-Δ)^{α/2} on an open subset in ℝ^d with zero exterior condition. We establish sharp two-sided estimates for the
Zhen-Qing Chen, Panki Kim, Renming Song
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Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation [PDF]

The Annals of Probability, 2012
Published in at http://dx.doi.org/10.1214/11-AOP682 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Chen, Zhen-Qing, Kim, Panki, Song, Renming   +2 more
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The Dirichlet Heat Kernel in Inner Uniform Domains in Fractal-Type Spaces [PDF]

Potential Analysis, 2021
AbstractThis paper proves two-sided estimates for the Dirichlet heat kernel on inner uniform domains in metric measure Dirichlet spaces satisfying the volume doubling condition, the Poincaré inequality, and a cutoff Sobolev inequality. More generally, we obtain local upper and lower bounds for the Dirichlet heat kernel on locally inner uniform domains ...
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Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates [PDF]

Calculus of Variations and Partial Differential Equations, 2020
The notes arXiv:1806.03428 will be divided in a series of papers. This is the second paper dealing with strictly local Dirichlet forms. v2 corrects typos and changes some terminology. To appear in Cal.
Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen, Luke Rogers, Nageswari Shanmugalingam, Alexander Teplyaev   +5 more
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Dirichlet heat kernel in the exterior of a compact set

Communications on Pure and Applied Mathematics, 2001
Let \(M\) be a complete, noncompact Riemannian manifold. For a compact set \(K\subset M\) denote \(\Omega=M\setminus K\) and consider the Dirichlet heat kernel \(p_\Omega(t,x,y)\) in \(\Omega\) which by definition, as a function of \(t\) and \(x\), is a minimal positive solution of the problem \[ \partial_tu=\Delta u,\qquad u| _{\partial\Omega}=0 ...
Grigor'yan, A, Saloff-Coste, L
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Subexponential behaviour of the Dirichlet heat kernel

Journal of Functional Analysis, 2003
Let \(D\) be an open and connected set in \(\mathbb{R}^m\), and let \(p_D(x,y; t)\), \(x\in D\), \(y\in D\), \(t> 0\) denote the Dirichlet heat kernel associated to the parabolic operator \(-\Delta_D+ {\partial\over\partial t}\), where \(-\Delta_D\) is the Dirichlet Laplacian for \(D\).
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Dirichlet heat kernel estimates for $\Delta^{\alpha/2}+ \Delta^{\beta/2}$

Illinois Journal of Mathematics, 2010
For $d\geq 1$ and ...
Chen, Zhen-Qing, Kim, Panki, Song, Renming   +2 more
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Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms [PDF]

Advances in Mathematics, 2020
56 pages.
Chen, Zhen-Qing, Kumagai, Takashi, Wang, Jian   +2 more
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Heat-Semigroup-Based Besov Capacity on Dirichlet Spaces and Its Applications

Mathematics
In this paper, we investigate the Besov space and the Besov capacity and obtain several important capacitary inequalities in a strictly local Dirichlet space, which satisfies the doubling condition and the weak Bakry–Émery condition.
Xiangyun Xie, Haihui Wang, Yu Liu
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Gaussian bounds for the Dirichlet heat kernel

Journal of Functional Analysis, 1990
The author uses the semigroup property of the heat kernel associated with the Dirichlet Laplacian to establish a pointwise Gaussian lower bound for this kernel in an open set in m-dimensional space.
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