Geodesic
Harmonic morphisms and non-linear potential theory
Banach Center Publications, Tome 27 (1992) no. 1, pp. 271-275 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'acte

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].
DOI : 10.4064/-27-1-271-275

Ilpo Laine 1

1 
@article{10_4064__27_1_271_275,
     author = {Ilpo Laine},
     title = {Harmonic morphisms and non-linear potential theory},
     journal = {Banach Center Publications},
     pages = {271--275},
     year = {1992},
     volume = {27},
     number = {1},
     doi = {10.4064/-27-1-271-275},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/-27-1-271-275/}
}
TY  - JOUR
AU  - Ilpo Laine
TI  - Harmonic morphisms and non-linear potential theory
JO  - Banach Center Publications
PY  - 1992
SP  - 271
EP  - 275
VL  - 27
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/-27-1-271-275/
DO  - 10.4064/-27-1-271-275
LA  - en
ID  - 10_4064__27_1_271_275
ER  - 
%0 Journal Article
%A Ilpo Laine
%T Harmonic morphisms and non-linear potential theory
%J Banach Center Publications
%D 1992
%P 271-275
%V 27
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/-27-1-271-275/
%R 10.4064/-27-1-271-275
%G en
%F 10_4064__27_1_271_275
Ilpo Laine. Harmonic morphisms and non-linear potential theory. Banach Center Publications, Tome 27 (1992) no. 1, pp. 271-275. doi: 10.4064/-27-1-271-275

Cité par Sources :