Heat kernel analysis on diamond fractals
Heat kernel analysis on diamond fractals
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DOI：
10.1016/j.spa.2020.08.009
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发表时间：
2019-06
影响因子：
1.4
通讯作者：
Patricia Alonso Ruiz
中科院分区：
文献类型：
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作者：
Patricia Alonso Ruiz
本文对一类不满足体积加倍性质的（N× N）-参数紧致度量测度空间族的热核进行了详细的分析。特别地，研究了热核的一致界、其Lipschitz连续性以及相应热半群的连续性;给出了一个具体例子，揭示了对数修正。的估计，以获得感兴趣的功能不等式描述的收敛到平衡的扩散过程。
This paper presents a detailed analysis of the heat kernel on an (N× N)-parameter family of compact metric measure spaces which do not satisfy the volume doubling property. In particular, uniform bounds of the heat kernel, its Lipschitz continuity and the continuity of the corresponding heat semigroup are studied; a specific example is presented revealing a logarithmic correction. The estimates are applied to derive functional inequalities of interest in describing the convergence to equilibrium of the diffusion process.