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Heat kernel estimates for general boundary problems

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journal contribution
posted on 19.04.2016, 10:12 by Liangpan Li, Alexander Strohmaier
We show that not feeling the boundary estimates for heat kernels hold for any non-negative self-adjoint extension of the Laplace operator acting on vector-valued compactly supported functions on a domain in $\mathbb{R}^d$. They are therefore valid for any choice of boundary condition and we show that the implied constants can be chosen independent of the self-adjoint extension. The method of proof is very general and is based on finite propagation speed estimates and explicit Fourier Tauberian theorems obtained by Y. Safarov.

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  • Science

Department

  • Mathematical Sciences

Citation

LI, L. and STROHMAIER, A., Heat kernel estimates for general boundary problems. arXiv:1604.00784 [math.AP].

Publisher

arXiv.org

Version

SMUR (Submitted Manuscript Under Review)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2016

Notes

This is a preprint submitted to arXiv on 4th Apr 2016.

Language

en

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