
doi: 10.1007/bf03024402
A real-valued function \(u\) of \(n\) real variables is called harmonic in an \(n\)-dimensional domain if it satisfies Laplace's equation \(\nabla u=0\), where \(\nabla\) is the \(n\)-dimensional Laplace operator. Certain boundary conditions to be satisfied by \(u\) are familiar in the literature. One is Dirichlet's boundary condition, specifying the value of \(u\) on the boundary of the domain. Another is Neumann's boundary condition, specifying the normal derivative of \(u\) on the boundary. A third, less common, condition has become known in certain sources as Robin's condition: \(u\) should satisfy \(\partial u/\partial n+\alpha u=f(x)\) on the boundary of the domain, where \(\partial u/\partial n\) denotes the normal derivative of \(u\), \(\alpha\) is a positive constant, and \(f(x)\) is a given function. The purpose of this paper is to enquire into who this Robin was and also to see if there is any justification in attaching his name to this condition. Gustave Robin (1855-1897) was a professor of mathematical physics in Paris. He wrote his doctoral thesis under the guidance of Emile Picard. Its subject matter was the determination of an electrostatic potential on a convex surface and it required the solution of a Neumann-type boundary condition for a harmonic function. This seems to be the nearest connection to Robin's involvement in the third boundary condition. Robin published very little in his lifetime, although his Oeuvres scientifiques were published in three volumes shortly after his death, and his name has fallen into obscurity. The authors' main finding is that there is little reason to connect Robin's name with the third boundary condition, as he never explicitly worked on this problem. Russian literature from the 1920's mentions his name and contributions, but only in connection with the type of problem considered in his thesis. The authors also suggest that Stefan Bergman (1895-1977) was the first to attribute Robin's name to this third boundary condition, in 1948. A second part to this paper will examine Robin's work more closely.
History of mathematics in the 20th century, mathematical physics, harmonic function, History of mathematics in the 19th century, History of partial differential equations, Gustave Robin, third boundary condition
History of mathematics in the 20th century, mathematical physics, harmonic function, History of mathematics in the 19th century, History of partial differential equations, Gustave Robin, third boundary condition
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