Results 11 to 20 of about 423 (121)
Dirichlet Heat Kernel for the Laplacian in a Ball [PDF]
Potential Analysis, 2018 We provide sharp two-sided estimates on the Dirichlet heat kernel $k_1(t,x,y)$ for the Laplacian in a ball. The result accurately describes the exponential behaviour of the kernel for small times and significantly improves the qualitatively sharp results known so far.
Małecki, Jacek, Serafin, Grzegorz
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Estimates of heat kernels for non-local regular Dirichlet forms [PDF]
Transactions of the American Mathematical Society, 2014 In this paper we present new heat kernel upper bounds for a certain class of non-local regular Dirichlet forms on metric measure spaces, including fractal spaces. We use a new purely analytic method where one of the main tools is the parabolic maximum principle. We deduce an off-diagonal upper bound of the heat kernel from the on-diagonal one under the
Grigoryan, Alexander +2 more
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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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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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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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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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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 +2 more
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Heat kernel estimates for the fractional Laplacian with Dirichlet conditions
The Annals of Probability, 2010 Published in at http://dx.doi.org/10.1214/10-AOP532 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Bogdan, Krzysztof +2 more
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Laplace Dirichlet heat kernels in convex domains [PDF]
Journal of Differential Equations, 2022 We provide general lower and upper bounds for Laplace Dirichlet heat kernel of convex $\mathcal C^{1,1}$ domains. The obtained estimates precisely describe the exponential behaviour of the kernels, which has been known only in a few special cases so far. Furthermore, we characterize a class of sets for which the estimates are sharp, i.e.
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Ain Shams Engineering Journal, 2023 Under the time-variable Dirichlet condition, the time-fractional diffusion equation with heat absorption in a sphere is taken into consideration. The time-fractional derivative with the power-law kernel is used in the generalized Cattaneo constitutive ...
Nehad Ali Shah +4 more
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