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Estimées de gradients de fonctions propres de Dirichlet
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ARNAUDON, Marc | |
| hal.structure.identifier | Mathematics Research Unit | |
| dc.contributor.author | THALMAIER, Anton | |
| hal.structure.identifier | Tianjin University [TJU] | |
| dc.contributor.author | WANG, Feng-Yu | |
| dc.date.accessioned | 2024-04-04T03:05:21Z | |
| dc.date.available | 2024-04-04T03:05:21Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193238 | |
| dc.description.abstractEn | By methods of stochastic analysis on Riemannian manifolds, we derive explicit constants $c_1(D)$ and $c_2(D)$ for a $d$-dimensional compact Riemannian manifold $D$ with boundary such that $c_1(D)\sqrt{\lambda}\|\phi\|_\infty \le \|\nabla \phi\|_\infty\le c_2(D)\sqrt{\lambda} \|\phi\|_\infty$ holds for any Dirichlet eigenfunction $\phi$ of $-\Delta$ with eigenvalue $\lambda$. In particular, when $D$ is convex with nonnegative Ricci curvature, this estimate holds for $c_1(D)=\frac{1}{de}$ and $c_2(D)=\sqrt{e}\left(\frac{\sqrt{2}}{\sqrt{\pi}}+\frac{\sqrt{\pi}}{4\sqrt{2}}\right)$. Corresponding two-sided gradient estimates for Neumann eigenfunctions are derived in the second part of the paper. | |
| dc.language.iso | en | |
| dc.subject.en | AMS subject Classification: 35P20 | |
| dc.subject.en | 58J65 | |
| dc.subject.en | 60H30 | |
| dc.subject.en | Keywords: Eigenfunction | |
| dc.subject.en | gradient estimate | |
| dc.subject.en | diffusion process | |
| dc.subject.en | curvature | |
| dc.subject.en | second fundamental form | |
| dc.subject.en | second fundamental | |
| dc.subject.en | form | |
| dc.title | Estimées de gradients de fonctions propres de Dirichlet | |
| dc.title.en | Gradient Estimates on Dirichlet Eigenfunctions | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 1710.10832 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-01625890 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01625890v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.title=Estim%C3%A9es%20de%20gradients%20de%20fonctions%20propres%20de%20Dirichlet&rft.atitle=Estim%C3%A9es%20de%20gradients%20de%20fonctions%20propres%20de%20Dirichlet&rft.au=ARNAUDON,%20Marc&THALMAIER,%20Anton&WANG,%20Feng-Yu&rft.genre=preprint |
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