CHOULLI, Mourad; KAYSER, Laurent; MAATI OUHABAZ, El

doi:10.1017/S0004972715000611

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CHOULLI, Mourad
Institut Élie Cartan de Lorraine [IECL]

KAYSER, Laurent
Institut Élie Cartan de Lorraine [IECL]

MAATI OUHABAZ, El
Institut de Mathématiques de Bordeaux [IMB]

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Bulletin of the Australian Mathematical Society. 2015, vol. 92, n° 3, p. 429-439

John Loxton University of Western Sydney|Australia

Resumen en inglés

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.< Leer menos

Palabras clave en inglés

Neumann Laplacian

Gaussian bounds

Riemannian manifolds.

Heat kernels

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194455

DOI

http://dx.doi.org/10.1017/S0004972715000611

Proyecto ANR

Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013

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Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251