On the boundary limits of harmonic functions with gradient in L p
Annales de l'Institut Fourier, Volume 34 (1984) no. 1, p. 99-109

This paper deals with tangential boundary behaviors of harmonic functions with gradient in Lebesgue classes. Our aim is to extend a recent result of Cruzeiro (C.R.A.S., Paris, 294 (1982), 71–74), concerning tangential boundary limits of harmonic functions with gradient in L n (R + n ), R + n denoting the upper half space of the n-dimensional euclidean space R n . Our method used here is different from that of Nagel, Rudin and Shapiro (Ann. of Math., 116 (1982), 331–360); in fact, we use the integral representation of precise functions given by Ohtsuka (Lecture Notes, Hiroshima Univ., 1973).

Dans cet article on étudie l’allure tangentielle à la frontière des fonctions harmoniques dans la classe de Sobolev W 1 p (R + n ), où R + n est le demi-espace de R n . On donne une généralisation du résultat récent de Cruzeiro (C.R.A.S., Paris, 294 (1982), 71–74), dans le cas p=n. Ici on utilise la représentation intégrale des fonctions de Beppo-Levi de Ohtsuka (Lecture Notes, Hiroshima Univ., 1973), et notre méthode est différente de celle de Nagel, Rudin et Shapiro (Ann. of Math., 116 (1982), 331–360).

@article{AIF_1984__34_1_99_0,
     author = {Mizuta, Yoshihiro},
     title = {On the boundary limits of harmonic functions with gradient in $L^p$},
     journal = {Annales de l'Institut Fourier},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {34},
     number = {1},
     year = {1984},
     pages = {99-109},
     doi = {10.5802/aif.952},
     zbl = {0522.31009},
     mrnumber = {85f:31009},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1984__34_1_99_0}
}
Mizuta, Yoshihiro. On the boundary limits of harmonic functions with gradient in $L^p$. Annales de l'Institut Fourier, Volume 34 (1984) no. 1, pp. 99-109. doi : 10.5802/aif.952. http://www.numdam.org/item/AIF_1984__34_1_99_0/

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