Boundary properties of functions with finite Dirichlet integrals

Doob, J. L.

doi:10.5802/aif.126

Doob, J. L.

Annales de l'Institut Fourier, Tome 12 (1962), pp. 573-621.

Résumé

L’auteur étudie dans un espace de Green (en particulier un domaine borné de $R^{n}$ ) les fonctions $B L D$ (limites en un certain sens des fonctions assez régulières à intégrale de Dirichlet finie). On se ramène au cas harmonique montré qu’une telle fonction harmonique $u$ est solution d’un problème de Dirichlet-Martin (c’est-à-dire correspond à une donnée $u^{'}$ sur la frontière de Martin), ce qui entraîne l’existence d’une limite “fine” $u^{'}$ p.p. Cela résulte de travaux antérieurs et de la remarque que $u^{2}$ a une mesure de Riesz associée de total fini. Puis on exprime l’intégrale de Dirichlet de $u$ au moyen de $u^{'}$ , grâce à la fonction $Θ$ de la thèse Naïm. D’autre part, on introduit et utilise systématiquement des notions de dérivée normale généralisée à la frontière de Martin, permettant d’étendre divers problèmes classiques relatifs à une frontière euclidienne assez régulière.

MR Zbl | 7 citations dans Numdam

DOI : 10.5802/aif.126

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     title = {Boundary properties of functions with finite {Dirichlet} integrals},
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     mrnumber = {30 #3992},
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Doob, J. L. Boundary properties of functions with finite Dirichlet integrals. Annales de l'Institut Fourier, Tome 12 (1962), pp. 573-621. doi : 10.5802/aif.126. https://www.numdam.org/articles/10.5802/aif.126/

Bibliographie
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