Approximation of harmonic functions

Dahlberg, Björn E. J.

Annales de l'Institut Fourier, Tome 30 (1980), p. 97-107 / Harvested from Numdam

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Résumé
Abstract

Soit $D$ un domaine borné à frontière régulière, et $u$ une fonction harmonique dans $D$ . On montre que si les valeurs de $u$ à la frontière appartiennent à $L^{p} (σ)$ avec $p \geq 2$ ( $σ$ étant la mesure de surface à la frontière), $u$ est approchable uniformément par des fonctions à variation bornée, et on montre que le résultat ne s’étend pas au cas $p < 2$ .

Let $u$ be harmonic in a bounded domain $D$ with smooth boundary. We prove that if the boundary values of $u$ belong to $L^{p} (σ)$ , where $p \geq 2$ and $σ$ denotes the surface measure of $\partial D$ , then it is possible to approximate $u$ uniformly by function of bounded variation. An example is given that shows that this result does not extend to $p < 2$ .

Publié le : 1980-01-01

MR 82i:31010 | Zbl 0417.31005 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.787

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     author = {Dahlberg, Bj\"orn E. J.},
     title = {Approximation of harmonic functions},
     journal = {Annales de l'Institut Fourier},
     volume = {30},
     year = {1980},
     pages = {97-107},
     doi = {10.5802/aif.787},
     mrnumber = {82i:31010},
     zbl = {0417.31005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1980__30_2_97_0}
}

Dahlberg, Björn E. J. Approximation of harmonic functions. Annales de l'Institut Fourier, Tome 30 (1980) pp. 97-107. doi : 10.5802/aif.787. http://gdmltest.u-ga.fr/item/AIF_1980__30_2_97_0/

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