Small diffusion and short time asymptotics for Pucci's operators

This paper presents asymptotic formulas in the case of the following two problems for the Pucci's extremal operators . It is considered the solution of in Ω such that on Γ. Here, is a domain (not necessarily bounded) and Γ is its boundary. It is also considered the solution of in , v = 1 on and v = 0 on . In the spirit of their previous works [Berti D, Magnanini R. Asymptotics for the resolvent equation associated to the game-theoretic p-laplacian. Appl Anal. 2019;98(10):1827–1842.; Berti D, Magnanini R. Short-time behavior for game-theoretic p-caloric functions. J Math Pures Appl (9). 2019;(126):249–272.], the authors establish the profiles as ϵ or of the values of and as well as of those of their q-means on balls touching Γ. The results represent a further step in the extensions of those obtained by Varadhan and by Magnanini-Sakaguchi in the linear regime.