Fundamental Existence Theorems
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.
KeywordsManifold Lution Dition Verse Prolate
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- Picard, Trai U d’Analyse, 3rd ed. Paris 1922, Vol. I, pp. 226—233Google Scholar
- Lebesgue: Sur le Probleme de Dirichlet, Comptes Rendus de l’Academie de Paris, Vol. 154 (1912), p. 335Google Scholar
- Lebesgue, Comptes Rendus, Vol. 178 (1924), p. 352Google Scholar
- Bouligand, Bulletin des sciences mathematiques, Ser. 2, Vol. 48 (1924), p. 205.Google Scholar
- Wiener, N., Journal of Mathemat’s and Physics of the Massachusetts Institute of Technology, Vol. III (1924), p. 49Google Scholar
- Kellogg, Comptes Rendus de T Academie de Paris, Vol. 187 (1928), p. 526Google Scholar