Fundamental solutions and two properties of elliptic maximal and minimal operators

For a large class of nonlinear second order elliptic differential operators, we define a concept of dimension, upon which we construct a fundamental solution. This allows us to prove two properties associated to these operators, which are generalizations of properties for the Laplacian and Pucci's operators. If ${\mathcal M}$ denotes such an operator, the first property deals with the possibility of removing singularities of solutions to the equation

$${\mathcal M}(D^2 u)-u^p=0,$$    in $$\quad B\setminus \{0\},$$

where $B$ is a ball in $\mathbb{R}^N$. The second property has to do with existence or nonexistence of solutions in $R^N$ to the inequality

$${\mathcal M}(D^2 u)+u^p\le 0,$$    in $$\quad \mathbb{R}^N.$$

In both cases a common critical exponent defined upon the dimension number is obtained, which plays the role of $N/(N-2)$ for the Laplacian.