Maxwell's equations form the cornerstone of electromagnetic theory, offering a complete description of how electric and magnetic fields interact with matter. In combination with state‐of‐the‐art ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

Let (M,g) be a pseudo-Riemannian manifold of dimension n. Explicit formulas are given for (1) a fourth-order operator D4,k on k-forms in M, n ≠ 1,2,4, (2) a sixth-order operator D6 on functions, n ≠ 1 ...

American Journal of Mathematics, Vol. 132, No. 3 (June 2010), pp. 771-839 (69 pages) We uncover the full null structure of the Maxwell-Dirac system in Lorenz gauge. This structure, which cannot be ...