Observations on Gaussian upper bounds for Neumann heat kernels
| hal.structure.identifier | Institut Élie Cartan de Lorraine [IECL] | |
| dc.contributor.author | CHOULLI, Mourad | |
| hal.structure.identifier | Institut Élie Cartan de Lorraine [IECL] | |
| dc.contributor.author | KAYSER, Laurent | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MAATI OUHABAZ, El | |
| dc.date.accessioned | 2024-04-04T03:18:55Z | |
| dc.date.available | 2024-04-04T03:18:55Z | |
| dc.date.issued | 2015 | |
| dc.identifier.issn | 0004-9727 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194455 | |
| dc.description.abstractEn | Given a domain $\Omega$ of a complete Riemannian manifold $\mathcal{M}$ and define $\mathcal{A}$ to be the Laplacian with Neumann boundary condition on $\Omega$. We prove that, under appropriate conditions, the corresponding heat kernel satisfies the Gaussian upper bound$$h(t,x,y)\leq \frac{C}{\left[V_\Omega(x,\sqrt{t})V_\Omega (y,\sqrt{t})\right]^{1/2}}\left( 1+\frac{d^2(x,y)}{4t}\right)^{\delta}e^{-\frac{d^2(x,y)}{4t}},\;\; t>0,\; x,y\in \Omega .$$Here $d$ is the geodesic distance on $\mathcal{M}$, $V_\Omega (x,r)$ is the Riemannian volume of $B(x,r)\cap \Omega$, where $B(x,r)$ is the geodesic ball of center $x$ and radius $r$, and $\delta$ is a constant related to the doubling property of $\Omega$.As a consequence we obtain analyticity of the semigroup $e^{-t {\mathcal A}}$ on $L^p(\Omega)$ for all $p \in [1, \infty)$ as well as a spectral multiplier result. | |
| dc.description.sponsorship | Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013 | |
| dc.language.iso | en | |
| dc.publisher | John Loxton University of Western Sydney|Australia | |
| dc.subject.en | Neumann Laplacian | |
| dc.subject.en | Gaussian bounds | |
| dc.subject.en | Riemannian manifolds. | |
| dc.subject.en | Heat kernels | |
| dc.title.en | Observations on Gaussian upper bounds for Neumann heat kernels | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1017/S0004972715000611 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Mathématiques générales [math.GM] | |
| dc.identifier.arxiv | 1502.06740 | |
| bordeaux.journal | Bulletin of the Australian Mathematical Society | |
| bordeaux.page | 429-439 | |
| bordeaux.volume | 92 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01119643 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01119643v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Bulletin%20of%20the%20Australian%20Mathematical%20Society&rft.date=2015&rft.volume=92&rft.issue=3&rft.spage=429-439&rft.epage=429-439&rft.eissn=0004-9727&rft.issn=0004-9727&rft.au=CHOULLI,%20Mourad&KAYSER,%20Laurent&MAATI%20OUHABAZ,%20El&rft.genre=article |
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