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Simultaneous Solutions of the Weak Dirichlet Problem*

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Abstract

The main aim of this paper is a geometrical approach to simultaneous solutions of the abstract weak Dirichlet problem. We answer partially a question from the paper [2] where a similar problem was discussed from a potential-theoretical point of view for the case of function spaces consisting of harmonic functions.

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References

  1. Bliedtner, J. and Hansen, W.: 'Simplicial cones in potential theory', Inventiones Math. 29(1975), 83-110.

    Google Scholar 

  2. Bliedtner, J. and Hansen, W.: 'The weak Dirichlet problem', J. Reine Angew. Math. 348(1984), 34-39.

    Google Scholar 

  3. Kolář, J.: 'Simultaneous extension operators for the density topology', Real Anal. Exchange 25(1999/2000), 223-230.

    Google Scholar 

  4. Lazar, A.: 'Spaces of affine continuous functions on simplexes', Trans. Amer. Math. Soc. 134(1968), 503-525.

    Google Scholar 

  5. Lindenstrauss, J. and Tzafriri, L.: 'Classical Banach Spaces', Lecture Notes in Math. 338, Springer-Verlag, 1973.

  6. Lukeš, J., Malý, J. and Zajíček, L.: 'Fine topology methods in real analysis and potential theory', Lecture Notes in Math.1189, Springer-Verlag, 1986.

  7. Michael, E. and Pełczy´nski, A.: 'A linear extension theorem', Illinois J. Math. 11(1967), 563-579.

    Google Scholar 

  8. Werner, D.: 'Some lifting theorems for bounded linear operators', Functional analysis(Essen, 1991) (1994), Lecture Notes in Pure and Appl. Math. 150, 279- 291.

    Google Scholar 

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KolÁŘ, J., Lukeš, J. Simultaneous Solutions of the Weak Dirichlet Problem*. Potential Analysis 15, 17–21 (2001). https://doi.org/10.1023/A:1011256626660

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  • DOI: https://doi.org/10.1023/A:1011256626660

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