Dirichlet heat kernel - Open Access .click

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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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Pointwise monotonicity of heat kernels. [PDF]

Rev Mat Complut, 2023
Alonso-Orán D, Chamizo F, Martínez ÁD, Mas A. +3 more
europepmc +1 more source

On-diagonal Heat Kernel Lower Bound for Strongly Local Symmetric Dirichlet Forms

, 2016
This paper studies strongly local symmetric Dirichlet forms on general measure spaces. The underlying space is equipped with the intrinsic metric induced by the Dirichlet form, with respect to which the metric measure space does not necessarily satisfy volume-doubling property.
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Singular boundary behaviour and large solutions for fractional elliptic equations. [PDF]