Article ID: CBB941462998

Lebesgue’s criticism of Carl Neumann’s method in potential theory (2020)

unapi

In the 1870s, Carl Neumann proposed the so-called method of the arithmetic mean for solving the Dirichlet problem on convex domains. Neumann’s approach was considered at the time to be a reliable existence proof, following Weierstrass’s criticism of the Dirichlet principle. However, in 1937 H. Lebesgue pointed out a serious gap in Neumann’s proof. Curiously, the erroneous argument once again involved confusion between the notions of infimum and minimum. The objective of this paper is to show that Lebesgue’s sharp criticism of Neumann’s proof was only partially justified.

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Authors & Contributors
Gray, Jeremy
De Risi, Vincenzo
Enrico Rogora
Krzanowski, W. J.
Gambetta, Emanuele
Bingham, N. H.
Concepts
Mathematics
Philosophy of mathematics
Controversies and disputes
Philosophy of science
Contingency (philosophy)
Philosophy
Time Periods
19th century
20th century
20th century, early
17th century
Medieval
Ancient
Places
United States
Italy
Europe
Tuscany (Italy)
Institutions
Académie de Médecine, Paris
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