Pointwise estimates for heat kernels of convolution-type operators

Grigoryan A, Kondratiev Y, Piatnitski A, Zhizhina E (2018)
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY 117: 849-880.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor/in
Grigoryan, AlexanderUniBi; Kondratiev, YuriUniBi; Piatnitski, Andrey; Zhizhina, Elena
Abstract / Bemerkung
We study the large-time behaviour of the fundamental solution of parabolic equations with an elliptic part being non-local convolution-type operator. We assume that this operator is a generator of a Markov jump process, and that its convolution kernel decays at least exponentially at infinity. The fundamental solution shows rather different asymptotic behaviour depending on whether vertical bar x vertical bar less than or similar to root t, or root t << vertical bar x vertical bar << t, or vertical bar x vertical bar similar to t, or vertical bar x vertical bar >> t. In each of these regions we obtain sharp pointwise estimates for the fundamental solution.
Erscheinungsjahr
2018
Zeitschriftentitel
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
Band
117
Seite(n)
849-880
ISSN
0024-6115
eISSN
1460-244X
Page URI
https://pub.uni-bielefeld.de/record/2931989

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Grigoryan A, Kondratiev Y, Piatnitski A, Zhizhina E. Pointwise estimates for heat kernels of convolution-type operators. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY. 2018;117:849-880.
Grigoryan, A., Kondratiev, Y., Piatnitski, A., & Zhizhina, E. (2018). Pointwise estimates for heat kernels of convolution-type operators. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 117, 849-880. doi:10.1112/plms.12144
Grigoryan, A., Kondratiev, Y., Piatnitski, A., and Zhizhina, E. (2018). Pointwise estimates for heat kernels of convolution-type operators. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY 117, 849-880.
Grigoryan, A., et al., 2018. Pointwise estimates for heat kernels of convolution-type operators. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 117, p 849-880.
A. Grigoryan, et al., “Pointwise estimates for heat kernels of convolution-type operators”, PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, vol. 117, 2018, pp. 849-880.
Grigoryan, A., Kondratiev, Y., Piatnitski, A., Zhizhina, E.: Pointwise estimates for heat kernels of convolution-type operators. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY. 117, 849-880 (2018).
Grigoryan, Alexander, Kondratiev, Yuri, Piatnitski, Andrey, and Zhizhina, Elena. “Pointwise estimates for heat kernels of convolution-type operators”. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY 117 (2018): 849-880.