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Ouverts d"harmonicité pour les fonctions séparément harmoniques

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Abstract

Let D⊂ℝN, G⊂ℝM be two open sets, E⊂ D and F⊂ G two compact sets which satisfy the condition (H) (that is a harmonic condition similar to Leja"s condition). We find an open set Ω⊂ℝN+M such that each separately harmonic function f : X : = (D× F) ∪ (E × G) → ℝ (i.e.: for all x in E, f(x,.) is harmonic on G; for all y in F, f(., y) is harmonic on D) extends to a harmonic function on Ω.

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  1. Laboratoire de Mathématiques E. Picard, Université Paul Sabatier, 118 Route de Narbonne, F-31062, Toulouse, Cedex

    Jean-Marc Hécart

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  1. Jean-Marc Hécart
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Hécart, JM. Ouverts d"harmonicité pour les fonctions séparément harmoniques. Potential Analysis 13, 115–126 (2000). https://doi.org/10.1023/A:1008757804094

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