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

  • * Corresponding author: Peihe Wang

    * Corresponding author: Peihe Wang

The first author is supported by NSFC grant No. 11721101. The second author is supported by Shandong Provincial Natural Science Foundation ZR2020MA018

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  • In this paper, we establish global $ C^2 $ a priori estimates for solutions to the uniformly parabolic equations with Neumann boundary condition on the smooth bounded domain in $ \mathbb R^n $ 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.

    Mathematics Subject Classification: Primary: 35K55; Secondary: 35B40, 35K20.


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