Global $ C^2 $-estimates for smooth solutions to uniformly parabolic equations with Neumann boundary condition | Zendy

Zhenghuan Gao | Zendy; Peihe Wang | Zendy

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Global $ C^2 $-estimates for smooth solutions to uniformly parabolic equations with Neumann boundary condition

Author(s) -

Zhenghuan Gao,

Peihe Wang

Publication year - 2021

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.

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