A new Duhamel-type principle with applications to geometric (in)equalities
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910089934274560 |
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| author | Caselli, Michele Gennaioli, Luca |
| author_facet | Caselli, Michele Gennaioli, Luca |
| contents | We introduce a simple new method, based on the Caffarelli-Silvestre extension and a Duhamel-type formula, to derive exact pointwise identities for fractional commutators and nonlinear compositions associated with the fractional Laplacian on general Riemannian manifolds.
As applications, we obtain a pointwise fractional Leibniz rule, a fractional Bochner's formula with an explicit Ricci curvature term, apparently the first of this kind, and exact remainders in the Córdoba-Córdoba and Kato inequalities for the fractional Laplacian. All these formulas are new even in the Euclidean space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29823 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A new Duhamel-type principle with applications to geometric (in)equalities Caselli, Michele Gennaioli, Luca Analysis of PDEs We introduce a simple new method, based on the Caffarelli-Silvestre extension and a Duhamel-type formula, to derive exact pointwise identities for fractional commutators and nonlinear compositions associated with the fractional Laplacian on general Riemannian manifolds. As applications, we obtain a pointwise fractional Leibniz rule, a fractional Bochner's formula with an explicit Ricci curvature term, apparently the first of this kind, and exact remainders in the Córdoba-Córdoba and Kato inequalities for the fractional Laplacian. All these formulas are new even in the Euclidean space. |
| title | A new Duhamel-type principle with applications to geometric (in)equalities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.29823 |