We consider a nonlinear coupled system of partial differential equations with asymptotic boundary conditions which is relevant in the field of general relativity. Specifically, the PDE system relates the factors of a conformally flat spatial metric obeying the laws of gravity and electromagnetism to its charge and mass distributions. The solution to the system is shown to be existent, smooth, and unique. While the discussion of the PDE assumes knowledge of physics and differential geometry, the proof uses only the PDE theory of flat space.
"Existence and Uniqueness of Solutions of an Einstein-Maxwell PDE System,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 18:
1, Article 10.
Available at: https://scholar.rose-hulman.edu/rhumj/vol18/iss1/10