no. 2
On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold
Annales de l'Institut Fourier, Tome 28 (1978) no. 2, pp. 25-52.

Soit D⊂R n un domaine borné à frontière lipschitzienne. On montre que 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⊂X un domaine relativement compact à frontière lipschitzienne. On a alors que 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⊂R n is shown to be 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⊂X be open relatively compact, connected, with Lipschitz boundary. Then 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.

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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},
     pages = {25--52},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {28},
     number = {2},
     year = {1978},
     doi = {10.5802/aif.688},
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     mrnumber = {58 #6302},
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Taylor, John C. On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold. Annales de l'Institut Fourier, Tome 28 (1978) no. 2, pp. 25-52. doi : 10.5802/aif.688. https://aif.centre-mersenne.org/articles/10.5802/aif.688/

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