【online】On the vanishing discount problem from the negative direction
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题目: On the vanishing discount problem from the negative direction
报告人: Andrea Davini（University of Rome La Sapienza）
时间: 2020年11月17日 16:00 -17:00
报告方式: Zoom APP ID：650 6594 4606 密码：472578
摘要：It has been proved in A. Davini, A. Fathi, R. Iturriaga and M. Zavidovique, Invent. Math. (2016) that the unique viscosity solution of
uniformly converges, for λ→0+, to a specific solution u0 of the critical equation
where M is a closed and connected Riemannian manifold and c(H) is the critical value.
In this seminar, we will consider the same problem for λ→0−. In this case, viscosity solutions of equation (*) are not unique, in general, so we focus on the asymptotics of the minimal solution uλ− of (*). Under the assumption that constant functions are subsolutions of the critical equation, we prove that the uλ−also converges to u0 as λ→0−. Furthermore, we exhibit an example of H for which equation (*) admits a unique solution for λ<0 as well. The talk is based on a joint work with Lin Wang (Tsinghua University).