Sublinear Elliptic Operators

Abstract

We investigate second order elliptic equations \[F(\mathcal{H}u) = 0\] where the function $F\colon S(n)\to\mathbb{R}$ on the space of symmetric $n\times n$ matrices is assumed to be sublinear. There is very little to be found in the literature devoted particularly to sublinear elliptic operators. When examples of such operators occur, they are often merely treated as members of the larger class of convex operators. That class has been thoroughly investigated and many of its aspects are well understood. There is, however, something to be said about sublinear operators that do not, in general, apply to convex operators.