Geodesic
Harmonic morphisms and non-linear potential theory
Banach Center Publications, Tome 27 (1992) no. 1, pp. 271-275.

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

Ilpo Laine 1

1 
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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. http://geodesic.mathdoc.fr/articles/10.4064/-27-1-271-275/

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