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.
KeywordsHarmonic Function Boundary Point Dirichlet Problem Normal Derivative Closed Region
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