Robust Near-Diagonal Green Function Estimates
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 Dirichle...
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| Published in: | International mathematics research notices 2023-10, Vol.2023 (19), p.16957-16993 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | eng |
| Online Access: | Get full text |
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| Summary: | 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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| ISSN: | 1073-7928 1687-0247 |