A maximal regular boundary for solutions of elliptic differential equations
Loeb, Peter ; Walsh, Bertram
Annales de l'Institut Fourier, Tome 18 (1968), p. 283-308 / Harvested from Numdam
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Soit 𝒜 une classe harmonique de Brelot, définie sur W. Il est donné un critère de régularité en termes de barrières, pour les points d’une frontière idéale. Soit ℌ un sous-treillis banachique de ℬ𝒜 W . Si 𝒜 est hyperbolique, la frontière idéale compactifiante déterminée par ℌ contient une “frontière harmonique” Γ ℌ qui satisfait le critère de régularité et ℌ≅𝒞 R (Γ ℌ ). Entre autres applications, on a la théorie des frontières de Wiener et Royden et des comparaisons de classes harmoniques.

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     author = {Loeb, Peter and Walsh, Bertram},
     title = {A maximal regular boundary for solutions of elliptic differential equations},
     journal = {Annales de l'Institut Fourier},
     volume = {18},
     year = {1968},
     pages = {283-308},
     doi = {10.5802/aif.284},
     mrnumber = {39 \#4423},
     zbl = {0167.40302},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1968__18_1_283_0}
}

Loeb, Peter; Walsh, Bertram. A maximal regular boundary for solutions of elliptic differential equations. Annales de l'Institut Fourier, Tome 18 (1968) pp. 283-308. doi : 10.5802/aif.284. http://gdmltest.u-ga.fr/item/AIF_1968__18_1_283_0/

[1] M. Brelot, Lectures on Potential Theory, Tata Inst. of Fundamental Research, Bombay, 1960. | MR 118980 | MR 22 #9749 | Zbl 0098.06903

[2] C. Constantinescu and A. Cornea, Ideale Ränder Riemannscher Flächen, Ergebnisse der Math. (2) 32 (1963). | MR 159935 | Zbl 0112.30801

[3] C. Constantinescu and A. Cornea, Compactifications of harmonic spaces, Nagoya Math. J. 25 (1965), 1-57. | MR 174760 | MR 30 #4960 | Zbl 0138.36701

[4] S. Kakutani, Concrete representation of abstract (M)-spaces, Ann. of Math. (2) 42 (1941), 994-1024. | MR 5778 | Zbl 0061.24209 | Zbl 0060.26604

[5] P.A. Loeb, An axiomatic treatment of pairs of elliptic differential equations, Ann. Inst. Fourier (Grenoble) 16,2 (1966), 167-208. | Numdam | MR 227455 | MR 37 #3039 | Zbl 0172.15101

[6] P.A. Loeb, A minimal compactification for extending continuous functions, Proc. Amer. Math. Soc. 18,2 (1967), 282-283. | MR 216468 | MR 35 #7301 | Zbl 0146.44503

[7] P.A. Loeb and B. Walsh, The equivalence of Harnack's principle and Harnack's inequality in the axiomatic system of Brelot, Ann. Inst. Fourier (Grenoble) 15 (1965), 597-600. | Numdam | MR 190360 | MR 32 #7773 | Zbl 0132.33802

[8] L. Lumer-Naïm, Harmonic product and harmonic boundary for bounded complex-valued harmonic functions, Abstract 623-18, Notices Amer. Math. Soc. 12 (1965), 355.

[9] I.E. Segal, Decompositions of operator algebras, I, Memoirs Amer. Math. Soc. 9 (1951). | MR 44749 | MR 13,472a | Zbl 0043.11505

[10] J.C. Taylor, The Feller and Šilov boundaries of a vector lattice, Illinois J. Math. 10 (1966), 680-693. | MR 34 #594 | Zbl 0143.15103

[11] B. Walsh and P.A. Loeb, Nuclearity in axiomatic potential theory, Bull. Amer. Math. Soc. 72 (1966), 685-689. | MR 35 #407 | Zbl 0144.15503