On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold
Annales de l'Institut Fourier, Volume 28 (1978) no. 2, p. 25-52
The Martin compactification of a bounded Lipschitz domain DR 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 MX 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.
Soit DR 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 MX 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.
@article{AIF_1978__28_2_25_0,
     author = {Taylor, John C.},
     title = {On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {28},
     number = {2},
     year = {1978},
     pages = {25-52},
     doi = {10.5802/aif.688},
     zbl = {0363.31010},
     mrnumber = {58 \#6302},
     language = {en},
     url = {http://www.numdam.org/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, Volume 28 (1978) no. 2, pp. 25-52. doi : 10.5802/aif.688. http://www.numdam.org/item/AIF_1978__28_2_25_0/

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