Volume 37_1-2_(2016)_63-104

Characterizing the strong maximum principle for constant coefficient subequations
REESE HARVEY - HERBERT BLAINE LAWSON JR.

Abstract. In this paper we characterize the degenerate elliptic equations F(D2u) = 0 whose subsolutions (F(D2u) ≥ 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 is in the spirit of previous work characterizing the ordinary maximum principle in terms of the geometry of the set of symmetric matrices F = {F ≥ 0}. Along the way, radial subsolutions are characterized, and, as an application, a sufficient condition for strong comparison is established. A number of examples, important for the theory of such equations, are examined.

Rend. Mat. Appl. (7) 37 (2016) 63-104;  pdf