Love--Lieb integral equations: applications, theory, approximations, and computation

Leandro Farina, Guillaume Lang, P. A. Martin

This paper is concerned mainly with the deceptively simple integral equation \[ u(x) - \frac{1}π\int_{-1}^{1} \frac{α\, u(y)}{α^2+(x-y)^2} \, \rd y = 1, \quad -1 \leq x \leq 1, \]…