Comparisons of kernel functions boundary Harnack principle and relative Fatou theorem on Lipschitz domains
Annales de l'Institut Fourier, Volume 28 (1978) no. 4, p. 147-167

On a Lipschitz domain D in R n , 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 D. The third theorem, on non-tangential limits of quotient of two positive harmonic functions in D, generalizes Doob’s relative Fatou theorem on a sphere. The main tools are maximum principle, Harnack inequality and differentiation of measures.

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.

@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},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {28},
     number = {4},
     year = {1978},
     pages = {147-167},
     doi = {10.5802/aif.719},
     zbl = {0368.31006},
     mrnumber = {80g:31005},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 28 (1978) no. 4, pp. 147-167. doi : 10.5802/aif.719. http://www.numdam.org/item/AIF_1978__28_4_147_0/

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