Solution representation formula and Hopf lemma to Pucci’s equation

Abstract.: We establish the existence of a viscosity subsolution along with its representation formula to the equation involving Pucci’s extremal operator (Formula presented.) with zero-th order term. We use a method based on a dynamic programming principle presented by Denis et-al. (Potential Analysis, 34(2), (2010), 139–161). As an application of our solution representation formula, we prove the Hopf lemma for (Formula presented.) with zero-th order term. Our approach is based on stochastic calculus and probabilistic methods.