On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold

Taylor, John C.

Taylor, John C.

Annales de l'Institut Fourier, Tome 28 (1978), p. 25-52 / Harvested from Numdam

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Résumé
Abstract

Soit $D \subset R^{n}$ un domaine borné à frontière lipschitzienne. On montre que $\bar{D}$ est le compactifié de Martin pour une classe assez étendue d’opérateurs uniformément elliptiques aux dérivées partielles d’ordre deux.

Soient $X$ une variété riemannienne ouverte et $M \subset X$ un domaine relativement compact à frontière lipschitzienne. On a alors que $\bar{M}$ est le compactifié de Martin défini par la restriction au domaine $D$ de l’opérateur de Laplace-Beltrami sur $X$ . Par conséquent, à chaque variété riemannienne ouverte $X$ on peut associer au plus une variété riemannienne compact à bord dont $X$ est l’intérieur.

The Martin compactification of a bounded Lipschitz domain $D \subset R^{n}$ is shown to be $\bar{D}$ for a large class of uniformly elliptic second order partial differential operators on $D$ .

Let $X$ be an open Riemannian manifold and let $M \subset X$ be open relatively compact, connected, with Lipschitz boundary. Then $\bar{M}$ is the Martin compactification of $M$ associated with the restriction to $M$ of the Laplace-Beltrami operator on $X$ . Consequently an open Riemannian manifold $X$ has at most one compactification which is a compact Riemannian manifold with boundary whose interior is $X$ .

Publié le : 1978-01-01

MR 58 #6302 | Zbl 0363.31010 | 3 citations dans Numdam

DOI : https://doi.org/10.5802/aif.688

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     author = {Taylor, John C.},
     title = {On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold},
     journal = {Annales de l'Institut Fourier},
     volume = {28},
     year = {1978},
     pages = {25-52},
     doi = {10.5802/aif.688},
     mrnumber = {58 \#6302},
     zbl = {0363.31010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1978__28_2_25_0}
}

Taylor, John C. On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold. Annales de l'Institut Fourier, Tome 28 (1978) pp. 25-52. doi : 10.5802/aif.688. http://gdmltest.u-ga.fr/item/AIF_1978__28_2_25_0/

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