Approximation of harmonic functions

Dahlberg, Björn E. J.. "Approximation of harmonic functions." Annales de l'institut Fourier 30.2 (1980): 97-107. <http://eudml.org/doc/74453>.

@article{Dahlberg1980,
abstract = {Let $u$ be harmonic in a bounded domain $D$ with smooth boundary. We prove that if the boundary values of $u$ belong to $L^p(\sigma )$, where $p\ge 2$ and $\sigma $ 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 $p&lt; 2$.},
author = {Dahlberg, Björn E. J.},
journal = {Annales de l'institut Fourier},
keywords = {approximation of harmonic functions; boundary values; functions of bounded variation},
language = {eng},
number = {2},
pages = {97-107},
publisher = {Association des Annales de l'Institut Fourier},
title = {Approximation of harmonic functions},
url = {http://eudml.org/doc/74453},
volume = {30},
year = {1980},
}

TY - JOUR
AU - Dahlberg, Björn E. J.
TI - Approximation of harmonic functions
JO - Annales de l'institut Fourier
PY - 1980
PB - Association des Annales de l'Institut Fourier
VL - 30
IS - 2
SP - 97
EP - 107
AB - Let $u$ be harmonic in a bounded domain $D$ with smooth boundary. We prove that if the boundary values of $u$ belong to $L^p(\sigma )$, where $p\ge 2$ and $\sigma $ 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 $p&lt; 2$.
LA - eng
KW - approximation of harmonic functions; boundary values; functions of bounded variation
UR - http://eudml.org/doc/74453
ER -