Harmonic morphisms and non-linear potential theory
Laine, Ilpo
Banach Center Publications, Tome 27 (1992), p. 271-275 / Harvested from The Polish Digital Mathematics Library
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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].

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:262739 
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Laine, Ilpo. Harmonic morphisms and non-linear potential theory. Banach Center Publications, Tome 27 (1992) pp. 271-275. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv27z1p271bwm/

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[003] [4] I. Laine, Introduction to a quasi-linear potential theory, ibid. 10 (1985), 339-348. | Zbl 0593.31013

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