Abstract
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.
AMS Classification 2010:
Disclosure statement
No potential conflict of interest was reported by the author(s).