Results 41 to 50 of about 62 (62)

Dirichlet heat kernel estimates for parabolic nonlocal equations

In this article we establish the optimal $C^s$ boundary regularity for solutions to nonlocal parabolic equations in divergence form in $C^{1,α}$ domains and prove a higher order boundary Harnack principle in this setting. Our approach applies to a broad class of nonlocal operators with merely Hölder continuous coefficients, but our results are new even
Svinger, Philipp, Weidner, Marvin
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NASH-TYPE INEQUALITIES AND HEAT KERNELS FOR NON-LOCAL DIRICHLET FORMS

Kyushu Journal of Mathematics, 2006
We use an elementary method to obtain Nash-type inequalities for non- local Dirichlet forms on d-sets. We obtain two-sided estimates for the corresponding heat kernels if the walk dimensions of heat kernels are less than two; these estimates are obtained by combining probabilistic and analytic methods.
Jiaxin HU, Takashi KUMAGAI
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Heat kernel estimates for Dirichlet fractional Laplacian with gradient perturbation

, 2017
We give a direct proof of the sharp two-sided estimates, recently established in [4,9], for the Dirichlet heat kernel of the fractional Laplacian with gradient perturbation in $C^{1, 1}$ open sets by using Duhamel formula. We also obtain a gradient estimate for the Dirichlet heat kernel. Our assumption on the open set is slightly weaker in that we only
Chen, Peng, Song, Renming, Xie, Longjie, Xie, Yingchao   +3 more
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Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians

Journal of Functional Analysis, 1984
The authors investigate connections between integral kernels of positivity preserving semigroups and \(L^ p\)-contractivity properties. There are treated essentially four connected topics: (1) Extension properties for \(e^{-tA}\) from \(L^ 2\) to \(L^{\infty}\) where A is a Schrödinger operator generated by its ground state.
Davies, E.B, Simon, B
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Dirichlet eigenfunction and heat kernel estimates on annular domains

43 pages, 5 ...
Chao, Brian, Saloff-Coste, Laurent
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Analysis of the heat kernel of the Dirichlet-to-Neumann operator

Journal of Functional Analysis, 2014
We prove Poisson upper bounds for the kernel $K$ of the semigroup generated by the Dirichlet-to-Neumann operator if the underlying domain is bounded and has a $C^\infty$-boundary. We also prove Poisson bounds for $K_z$ for all $z$ in the right half-plane and for all its derivatives.
ter Elst, A. F. M., Ouhabaz, E. M.
openaire   +2 more sources

Non-symmetric stable processes: Dirichlet heat kernel, Martin kernel and Yaglom limit

Stochastic Processes and their Applications
26 pages, 1 ...
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Dirichlet heat kernel estimates for a large class of anisotropic Markov processes

Electronic Journal of Probability
Let $Z=(Z^{1}, \ldots, Z^{d})$ be the d-dimensional Lévy {process} where {$Z^i$'s} are independent 1-dimensional Lévy {processes} with identical jumping kernel $ ν^1(r) =r^{-1}ϕ(r)^{-1}$. Here $ϕ$ is {an} increasing function with weakly scaling condition of order $\underline α, \overline α\in (0, 2)$.
Kim, Kyung-Youn, Wang, Lidan
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Spectral bounds and heat kernel upper estimates for Dirichlet forms

We use a Harnack-type inequality on exit times and spectral bounds to characterize upper bounds of the heat kernel associated with any regular Dirichlet form without killing part, where the scale function may vary with position. We further show that this Harnack-type inequality is preserved under quasi-symmetric changes of metric on uniformly perfect ...
Chen, Aobo, Yu, Zhenyu
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Dirichlet heat kernel estimates for fractional Laplacian under non-local perturbation

, 2015
For $d\ge 2$ and $0\varepsilon\}} (f(x+z)-f(x))\frac{b(x,z)}{|z|^{d+ }}\,dz, $$ and $b(x,z)$ is a bounded measurable function on $\mathbb{R}^{d}\times\mathbb{R}^{d}$ with $b(x,z)=b(x,-z)$ for every $x,z\in\mathbb{R}^{d}$. Here ${\cal A}(d, - )$ is a normalizing constant so that $\mathcal{S}^b=-(- )^{ /2}$ when $b(x, z)\equiv 1$.
Chen, Zhen-Qing, Yang, Ting
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