学术报告

【online】On the vanishing discount problem from the negative direction

发布人:发布时间: 2020-11-03

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题目: On the vanishing discount problem from the negative direction


报告人: Andrea DaviniUniversity of Rome La Sapienza


时间: 2020年11月17日  16:00 -17:00 


报告方式: Zoom APP  ID650 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

(*)λuλ+H(x,dxuλ)=c(H)in M,


uniformly converges, for λ→0+, to a specific solution u0 of the critical equation

H(x,dxu)=c(H)in M,


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).


邀请人:程伟 老师