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The wiener type solution of the Dirichlet problem in potential theory

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References

  1. Bauer, H.: Harmonische Räume und ihre Potentialtheorie. Berlin, Heidelberg, New York: Springer 1966

    Google Scholar 

  2. Bliedtner, J., Hansen, W.: Simplicial cones in potential theory. Invent. Math.29, 83–110 (1975)

    Google Scholar 

  3. Brelot, M.: Familles de Perron et problème de Dirichlet. Acta Sci. Math. (Szeged)9, 133–153 (1938–1940)

    Google Scholar 

  4. Brelot, M.: Sur un théorème du prolongement fonctionnel de Keldych concernant le problème de Dirichlet. J. Analyse Math.8, 273–288 (1961)

    Google Scholar 

  5. Brelot, M.: Axiomatique des fonctions harmoniques. Montréal: Les Presses de l'Université de Montréal 1966

    Google Scholar 

  6. Constantinescu, C., Cornea, A.: Potential theory on harmonic spaces. Berlin, Heidelberg, New York: Springer 1972

    Google Scholar 

  7. Hervé, R.-M.: Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel. Ann. Inst. Fourier12, 415–571 (1962)

    Google Scholar 

  8. Keldych, M. V.: On the resolutivity and the stability of Dirichlet problem (Russian). Uspechi Mat. Nauk8, 172–231 (1941)

    Google Scholar 

  9. Keldych, M. V.: On the Dirichlet problem. Dokl. Akad. Nauk SSSR32, 308–309 (1941)

    Google Scholar 

  10. Landis, E. M.: Necessary and sufficient conditions for the regularity of a boundary point for the Dirichlet problem for the heat equation (Russian). Dokl. Akad. Nauk SSSR185, 517–520 (1969)

    Google Scholar 

  11. Landis, E. M.: Equations of the second order of elliptic and parabolic types (Russian). Nauka, Moscow 1971

    Google Scholar 

  12. Lukeš, J.: Théorème de Keldych dans la théorie axiomatique de Bauer des fonctions harmoniques. Czech. Math. J.24, 114–125 (1974)

    Google Scholar 

  13. Monna, A. F.: Note sur le problème de Dirichlet. Nieuw Arch. Wiskunde19, 58–64 (1971)

    Google Scholar 

  14. Perron, O.: Eine neue Behandlung der ersten Randwertaufgabe für Δu=0. Math. Z.18, 42–54 (1923)

    Google Scholar 

  15. Remak, R.: Über potentialkonvexe Funktionen. Math. Z.20, 126–130 (1924)

    Google Scholar 

  16. Sternberg, W.: Über die Gleichung der Wärmeleitung. Math. Ann.101, 394–398 (1929)

    Google Scholar 

  17. Wiener, N.: Certain notions in potential theory. J. Math. Mass.3, 24–51 (1924)

    Google Scholar 

  18. Wiener, N.: Note on a paper of O. Perron. J. Math. Mass.4, 21–32 (1925)

    Google Scholar 

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Lukeš, J., Netuka, I. The wiener type solution of the Dirichlet problem in potential theory. Math. Ann. 224, 173–178 (1976). https://doi.org/10.1007/BF01436200

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