Local Nash Inequality and Inhomogeneity of Heat Kernels

By Jun Kigami. 2004

61 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/889c3c63a4af311361b8352da05ae3eb66c626f5

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In Applied Mathematics

1. Takashi Kumagai
2. Alexander Grigorʼyan
3. Martin T. Barlow
4. Jiaxin Hu
5. András Telcs
6. T. Coulhon
7. Dorin Ervin Dutkay
8. Zhen-Qing Chen

In Mathematical Physics

1. Alexander Grigorʼyan
2. Martin T. Barlow
3. Jiaxin Hu
4. Takashi Kumagai
5. T. Coulhon
6. András Telcs
7. Dorin Ervin Dutkay
8. Adam S. Sikora

Citations in the corpus

• Heat kernel upper bounds for jump processes and the first exit time (2009, background): “The implication (1) ⇒ (2) was proved in [15], while (2) ⇒ (3) ⇒ (1) is contained in [1]; see also [15] and [11] for more general results of this kind.”
• A new approach to pointwise heat kernel upper bounds on doubling metric measure spaces (2013, background): “for m > 2, and they can be characterised by Faber-Krahn type inequalities together with exit time estimates (see for instance [45], [37], and the references therein).”
• Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces (2008, background): “All known so far results have used some probabilistic conditions such as the first exit time from a ball, etc. ‐ cf. [2, 13, 16 ].”
• Heat kernels and function theory on metric measure spaces (2003, background): “2), and for that we refer the reader to [7], [12], [19], [20], [21], [24].”
• Upper Bounds of Heat Kernels on Doubling Spaces (2014, methodology): “[22] Kigami J., “Analysis on fractals”, Cambridge University Press, 2001.”
• TWO-SIDED ESTIMATES OF HEAT KERNELS ON METRIC MEASURE SPACES (2012, methodology): “(DUE ) Using (FK ), we obtain first some diagonal upper bound for the Dirichlet heat kernels in balls, and then use Kigami’s iteration argument and (1.13) to pass to (DUE).”
• Analysis of orthogonality and of orbits in affine iterated function systems (2006, methodology): “Two approaches to IFSs have been popular, one based on a discrete version of the more familiar and classical second order Laplace differential operator of potential theory, see [KSW01, Kig04 , LNRG96]; and the second approach is based on Fourier series, see e.g., [JoPe98, DuJo05].”