From Attraction Theory to Existence Proofs: The Evolution of Potential-Theoretic Methods in the Study of Boundary-Value Problems, 1860–1890
This paper examines developments in the study of boundary-value problems between about 1860 and 1890, in the context of the general evolution of this theory from the physical models in which the subject has its roots to a free-standing part of pure mathematics. The physically-motivated work of Carl Neumann and his method of the arithmetic mean appear as an initial phase in this development, one which employs physical models as an integral part of its reasoning and which concentrates on geometrical...