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arXiv · 2111.05768

Robust near-diagonal Green function estimates

Moritz Kassmann·Minhyun Kim·Ki-Ahm Lee
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Abstract

We prove sharp near-diagonal pointwise bounds for the Green function $G_\Omega(x,y)$ for nonlocal operators of fractional order $\alpha \in (0,2)$. The novelty of our results is two-fold: the estimates are robust as $\alpha \to 2-$ and we prove the bounds without making use of the Dirichlet heat kernel $p_\Omega(t;x,y)$. In this way we can cover cases, in which the Green function satisfies isotropic bounds but the heat kernel does not.

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Moritz Kassmann, Minhyun Kim, Ki-Ahm Lee. 2021-11-10. Robust near-diagonal Green function estimates. https://doi.org/10.1093/imrn%2Frnad106

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