Nous obtenons trois théorèmes sur les fonctions harmoniques dans un domaine lipschitzien : un principe du type de Harnack sur la frontière ; des inégalités géométriques pour le noyau de Poisson d’un tel domaine ; un théorème relatif de Fatou. Les outils essentiels sont le principe du maximum, l’inégalité de Harnack, et la dérivation des mesures.
On a Lipschitz domain in , three theorems on harmonic functions are proved. The first (boundary Harnack principle) compares two positive harmonic functions at interior points near an open subset of the boundary where both functions vanish. The second extends some familiar geometric facts about the Poisson kernel on a sphere to the Poisson kernel on . The third theorem, on non-tangential limits of quotient of two positive harmonic functions in , generalizes Doob’s relative Fatou theorem on a sphere. The main tools are maximum principle, Harnack inequality and differentiation of measures.
@article{AIF_1978__28_4_147_0,
author = {Wu, Jang-Mei G.},
title = {Comparisons of kernel functions boundary {Harnack} principle and relative {Fatou} theorem on {Lipschitz} domains},
journal = {Annales de l'Institut Fourier},
pages = {147--167},
publisher = {Institut Fourier},
address = {Grenoble},
volume = {28},
number = {4},
year = {1978},
doi = {10.5802/aif.719},
mrnumber = {80g:31005},
zbl = {0368.31006},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/aif.719/}
}
TY - JOUR AU - Wu, Jang-Mei G. TI - Comparisons of kernel functions boundary Harnack principle and relative Fatou theorem on Lipschitz domains JO - Annales de l'Institut Fourier PY - 1978 SP - 147 EP - 167 VL - 28 IS - 4 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.719/ DO - 10.5802/aif.719 LA - en ID - AIF_1978__28_4_147_0 ER -
%0 Journal Article %A Wu, Jang-Mei G. %T Comparisons of kernel functions boundary Harnack principle and relative Fatou theorem on Lipschitz domains %J Annales de l'Institut Fourier %D 1978 %P 147-167 %V 28 %N 4 %I Institut Fourier %C Grenoble %U http://archive.numdam.org/articles/10.5802/aif.719/ %R 10.5802/aif.719 %G en %F AIF_1978__28_4_147_0
Wu, Jang-Mei G. Comparisons of kernel functions boundary Harnack principle and relative Fatou theorem on Lipschitz domains. Annales de l'Institut Fourier, Tome 28 (1978) no. 4, pp. 147-167. doi : 10.5802/aif.719. http://archive.numdam.org/articles/10.5802/aif.719/
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