In this paper we characterize the degenerate elliptic equations F(Du) = 0 whose subsolutions (F(Du) ≥ 0) satisfy the strong maximum principle. We introduce an easily computed function f on (0,∞) which is determined by F, and we show that the strong maximum principle holds depending on whether ∫ 0+ dy f(y) is infinite or finite. This complements our previous work characterizing when the (ordinar...

We state a maximum principle for the gradient of the minima of integral functionals I (u)G Ω [ f (∇u)Cg(u)] dx, on ūCW 1,1 0 (Ω ), just assuming that I is strictly convex. We do not require that f, g be smooth, nor that they satisfy growth conditions. As an application, we prove a Lipschitz regularity result for constrained minima.

Gauge field theories may quite generally be defined as describing the coupling of a matter-field to an interaction-field, and they are suitably represented in the mathematical framework of fiber bundles. Their underlying principle is the socalled gauge principle, which is based on the idea of deriving the coupling structure of the fields by satisfying a postulate of local gauge covariance. The ...