Abstract
We consider the solution u of ut−ΔpGu=0 in a (not necessarily bounded) domain Ω, such that u=0 in Ω at time t=0 and u=1 on the boundary of Ω at all times. Here, ΔpG is the game-theoretic or normalizedp-laplacian. We derive new precise asymptotic formulas for t→0, that generalize that of S.R.S. Varadhan [39] for large deviations and that of the second author and S. Sakaguchi [26] for the heat content of a ball touching the boundary. We also determine the behavior for t→0 of the q-mean of u on such a ball. Applications to time-invariant level surfaces of u are then obtained.
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