Theory of Bessel potentials. III: Potentials on regular manifolds
Annales de l'Institut Fourier, Tome 19 (1969) no. 2, p. 279-338
On étudie ici les potentiels besseliens sur des variétés riemanniennes de classe C bordées ou ouvertes. Soient : M une variété n-dimensionnelle et N une sous-variété de M de dimension k. On donne des conditions suffisantes pour que : 1) la restriction à N d’un potentiel α sur M soit un potentiel d’ordre α-n-k 2 sur N ; 2) un potentiel d’ordre α-n-k 2 sur N admette une extension à un potentiel d’ordre α sur M. On prouve aussi que pour une variété bordée M la restriction à son intérieur M i est un isomorphisme isométrique entre l’espace des potentiels d’ordre α sur M, et l’espace des potentiels d’ordre α sur M i .
In this paper Bessel potentials on C -Riemannian manifolds (open or bordered) are studied. Let M be an n-dimensional manifold, and N a submanifold of M of dimension k. Sufficient conditions are given for: 1) the restriction to N of any potential of order α on M to be a potential of order α-n-k 2 on N ; 2) any potential of order α-n-k 2 on N to be extendable to a potential of order α on M. It is also proved that for a bordered manifold M the restriction to its interior M i is an isometric isomorphism between the spaces of potentials of order α on M and M i respectively.
@article{AIF_1969__19_2_279_0,
     author = {Adams, Robert and Aronszajn, Nachman and Hanna, M. S.},
     title = {Theory of Bessel potentials. III: Potentials on regular manifolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {19},
     number = {2},
     year = {1969},
     pages = {279-338},
     doi = {10.5802/aif.328},
     zbl = {0176.09902},
     mrnumber = {54 \#915},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1969__19_2_279_0}
}
Adams, Robert; Aronszajn, Nachman; Hanna, M. S. Theory of Bessel potentials. III: Potentials on regular manifolds. Annales de l'Institut Fourier, Tome 19 (1969) no. 2, pp. 279-338. doi : 10.5802/aif.328. http://www.numdam.org/item/AIF_1969__19_2_279_0/

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