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Asymptotic Lipschitz regularity of viscosity solutions of Hamilton-Jacobi equations


Authors: Xia Li and Lin Wang
Journal: Proc. Amer. Math. Soc. 146 (2018), 1571-1583
MSC (2010): Primary 35D40, 35F21, 37J50
DOI: https://doi.org/10.1090/proc/13816
Published electronically: December 28, 2017
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Abstract: For each continuous initial data $ \varphi (x)\in C(M,\mathbb{R})$, we obtain the asymptotic Lipschitz regularity of the viscosity solution of the following evolutionary Hamilton-Jacobi equation with convex and coercive Hamiltonians:

\begin{displaymath}\begin {cases}\partial _tu(x,t)+H(x,\partial _xu(x,t))=0,\\ u(x,0)=\varphi (x). \end{cases}\end{displaymath}    


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Additional Information

Xia Li
Affiliation: School of Mathematical and Physics, Suzhou University of Science and Technology, Suzhou Jiangsu, 215009, People’s Republic of China
Email: lixia0527@mail.usts.edu.cn

Lin Wang
Affiliation: Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, People’s Republic of China
Email: lwang@math.tsinghua.edu.cn

DOI: https://doi.org/10.1090/proc/13816
Keywords: Hamilton-Jacobi equations, viscosity solutions, asymptotic Lipschitz regularity
Received by editor(s): July 17, 2016
Received by editor(s) in revised form: May 3, 2017
Published electronically: December 28, 2017
Additional Notes: The first author was partially supported under NSFC Grant No. 11471238
The second author was partially supported under NSFC Grants No. 11631006, 11401107
Communicated by: Yingfei Yi
Article copyright: © Copyright 2017 American Mathematical Society

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