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On a gradient maximum principle for some quasilinear parabolic equations on convex domains


Author: Seonghak Kim
Journal: Proc. Amer. Math. Soc. 145 (2017), 1203-1208
MSC (2010): Primary 35B50, 35B65, 35K20, 35K59
DOI: https://doi.org/10.1090/proc/13291
Published electronically: September 15, 2016
MathSciNet review: 3589319
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Abstract: We establish a spatial gradient maximum principle for classical solutions to the initial and Neumann boundary value problem of some quasilinear parabolic equations on smooth convex domains.


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Seonghak Kim
Affiliation: Institute for Mathematical Sciences, Renmin University of China, Beijing 100872, People’s Republic of China
Email: kimseo14@ruc.edu.cn

DOI: https://doi.org/10.1090/proc/13291
Keywords: Quasilinear parabolic equation, gradient maximum principle, convex domain, Hopf's lemma, bootstrap of regularity
Received by editor(s): February 12, 2015
Received by editor(s) in revised form: May 13, 2016
Published electronically: September 15, 2016
Communicated by: Catherine Sulem
Article copyright: © Copyright 2016 American Mathematical Society

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