Abstract
As we saw in § 3 of Chapter IX (p. 237), Green, in 1828, inferred the existence of the function which bears his name from the assumption that a static charge could always be induced on a closed grounded con- ducting surface by a point charge within the conductor, and that the combined potential of the two charges would vanish on the surface. From this, he inferred the possibility of solving the Dirichlet problem. Such considerations could not, however, be accepted as an existence proof. In 1840, GAUSS gave the following argument. Let S denote the boundary of the region for which the Dirichlet problem is to’ be solved.
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References
Picard, Trai U d’Analyse, 3rd ed. Paris 1922, Vol. I, pp. 226—233
Lebesgue: Sur le Probleme de Dirichlet, Comptes Rendus de l’Academie de Paris, Vol. 154 (1912), p. 335
Lebesgue, Comptes Rendus, Vol. 178 (1924), p. 352
Bouligand, Bulletin des sciences mathematiques, Ser. 2, Vol. 48 (1924), p. 205.
Wiener, N., Journal of Mathemat’s and Physics of the Massachusetts Institute of Technology, Vol. III (1924), p. 49
Kellogg, Comptes Rendus de T Academie de Paris, Vol. 187 (1928), p. 526
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© 1929 Verlag Von Julius Springer
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Kellogg, O.D. (1929). Fundamental Existence Theorems. In: Foundations of Potential Theory. Die Grundlehren der Mathematischen Wissenschaften, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-90850-7_11
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