Abstract:
We establish the existence of a viscosity subsolution along with its representation formula to the equation involving Pucci’s extremal operator ℳ+𝜆,Λ 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 ℳ−𝜆,Λ with zero-𝑡ℎ order term. Our approach is based on stochastic calculus and probabilistic methods.