@article{Laine1992,
abstract = {Originally, harmonic morphisms were defined as continuous mappings φ:X → X' between harmonic spaces such that h'∘φ remains harmonic whenever h' is harmonic, see [1], p. 20. In general linear axiomatic potential theory, one has to replace harmonic functions h' by hyperharmonic functions u' in this definition, in order to obtain an interesting class of mappings, see [3], Remark 2.3. The modified definition appears to be equivalent with the original one, provided X' is a Bauer space, i.e., a harmonic space with a base consisting of regular sets, see [3], Theorem 2.4. To extend the linear proof of this result directly into the recent non-linear theories fails, even in the case of semi-classical non-linear considerations [6]. The aim of this note is to give a modified proof which settles such difficulties in the quasi-linear theories [4], [5].},
author = {Laine, Ilpo},
journal = {Banach Center Publications},
keywords = {harmonic morphisms; harmonic functions; hyperharmonic functions},
language = {eng},
number = {1},
pages = {271-275},
title = {Harmonic morphisms and non-linear potential theory},
url = {http://eudml.org/doc/262739},
volume = {27},
year = {1992},
}
TY - JOUR
AU - Laine, Ilpo
TI - Harmonic morphisms and non-linear potential theory
JO - Banach Center Publications
PY - 1992
VL - 27
IS - 1
SP - 271
EP - 275
AB - Originally, harmonic morphisms were defined as continuous mappings φ:X → X' between harmonic spaces such that h'∘φ remains harmonic whenever h' is harmonic, see [1], p. 20. In general linear axiomatic potential theory, one has to replace harmonic functions h' by hyperharmonic functions u' in this definition, in order to obtain an interesting class of mappings, see [3], Remark 2.3. The modified definition appears to be equivalent with the original one, provided X' is a Bauer space, i.e., a harmonic space with a base consisting of regular sets, see [3], Theorem 2.4. To extend the linear proof of this result directly into the recent non-linear theories fails, even in the case of semi-classical non-linear considerations [6]. The aim of this note is to give a modified proof which settles such difficulties in the quasi-linear theories [4], [5].
LA - eng
KW - harmonic morphisms; harmonic functions; hyperharmonic functions
UR - http://eudml.org/doc/262739
ER -
