Open AccessGlobal $ C^2 $-estimates for smooth solutions to uniformly parabolic equations with Neumann boundary condition
Author(s) -
Zhenghuan Gao,
Peihe Wang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2021152
Subject(s) - corollary , mathematics , domain (mathematical analysis) , bounded function , neumann boundary condition , boundary (topology) , a priori and a posteriori , viscosity , mathematical analysis , pure mathematics , physics , philosophy , epistemology , quantum mechanics
In this paper, we establish global \begin{document}$ C^2 $\end{document} a priori estimates for solutions to the uniformly parabolic equations with Neumann boundary condition on the smooth bounded domain in \begin{document}$ \mathbb R^n $\end{document} by a blow-up argument. As a corollary, we obtain that the solutions converge to ones which move by translation. This generalizes the viscosity results derived before by Da Lio.