The Martin compactification of a bounded Lipschitz domain is shown to be for a large class of uniformly elliptic second order partial differential operators on .
Let be an open Riemannian manifold and let be open relatively compact, connected, with Lipschitz boundary. Then is the Martin compactification of associated with the restriction to of the Laplace-Beltrami operator on . Consequently an open Riemannian manifold has at most one compactification which is a compact Riemannian manifold with boundary whose interior is .
Soit un domaine borné à frontière lipschitzienne. On montre que est le compactifié de Martin pour une classe assez étendue d’opérateurs uniformément elliptiques aux dérivées partielles d’ordre deux.
Soient une variété riemannienne ouverte et un domaine relativement compact à frontière lipschitzienne. On a alors que est le compactifié de Martin défini par la restriction au domaine de l’opérateur de Laplace-Beltrami sur . Par conséquent, à chaque variété riemannienne ouverte on peut associer au plus une variété riemannienne compact à bord dont 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}, pages = {25--52}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {28}, number = {2}, year = {1978}, doi = {10.5802/aif.688}, mrnumber = {58 #6302}, zbl = {0363.31010}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.688/} }
TY - JOUR AU - Taylor, John C. TI - On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold JO - Annales de l'Institut Fourier PY - 1978 SP - 25 EP - 52 VL - 28 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.688/ DO - 10.5802/aif.688 LA - en ID - AIF_1978__28_2_25_0 ER -
%0 Journal Article %A Taylor, John C. %T On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold %J Annales de l'Institut Fourier %D 1978 %P 25-52 %V 28 %N 2 %I Institut Fourier %C Grenoble %U http://archive.numdam.org/articles/10.5802/aif.688/ %R 10.5802/aif.688 %G en %F 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://archive.numdam.org/articles/10.5802/aif.688/
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