Displaying similar documents to “From Attraction Theory to Existence Proofs: The Evolution of Potential-Theoretic Methods in the Study of Boundary-Value Problems, 1860–1890”

30 Years of Calderón’s Problem

Gunther Uhlmann (2012-2013)

Séminaire Laurent Schwartz — EDP et applications

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In this article we survey some of the most important developments since the 1980 paper of A.P. Calderón in which he proposed the problem of determining the conductivity of a medium by making voltage and current measurements at the boundary.

On the boundary values of harmonic functions.

Paul R. Garabedian (1985)

Revista Matemática Iberoamericana

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Over the years many methods have been discovered to prove the existence of a solution of the Dirichlet problem for Laplace's equation. A fairly recent collection of proofs is based on representations of the Green's functions in terms of the Bergman kernel function or some equivalent linear operator [3]. Perhaps the most fundamental of these approaches involves the projection of an arbitrary function onto the class of harmonic functions in a Hilbert space whose norm is defined by the...

Naturphilosophie and its role in Riemann’s mathematics

Umberto Bottazzini, Rossana Tazzioli (1995)

Revue d'histoire des mathématiques

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This paper sets out to examine some of Riemann’s papers and notes left by him, in the light of the “philosophical” standpoint expounded in his writings on . There is some evidence that many of Riemann’s works, including his of 1854 on the foundations of geometry, may have sprung from his attempts to find a unified explanation for natural phenomena, on the basis of his model of the ether.

Solution of the Neumann problem for the Laplace equation

Dagmar Medková (1998)

Czechoslovak Mathematical Journal

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For fairly general open sets it is shown that we can express a solution of the Neumann problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series. If the open set is simply connected and bounded then the solution of the Dirichlet problem is the double layer potential with a density given by a similar series.