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Classical solutions of fully nonlinear parabolic equations

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Abstract

In this paper, we study the classical solutions of the fully nonlinear parabolic equation \({u_{t}-F(D_{x}^2u)=0,}\) where the nonlinear operator F is locally C 1,β almost everywhere with 0 < β < 1. The interior C 2,α regularity of the classical solutions will be shown without the assumption that F is convex (or concave).

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Authors and Affiliations

  1. College of Science, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Yi Cao & Dongsheng Li

  2. Department of Mathematics, The University of Iowa, Iowa, IA, 52242-1419, USA

    Lihe Wang

Authors
  1. Yi Cao
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  2. Dongsheng Li
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  3. Lihe Wang
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Correspondence to Yi Cao.

Additional information

This work was completed with the support of NSFC 10771166.

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Cao, Y., Li, D. & Wang, L. Classical solutions of fully nonlinear parabolic equations. Arch. Math. 95, 53–61 (2010). https://doi.org/10.1007/s00013-010-0142-0

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  • DOI: https://doi.org/10.1007/s00013-010-0142-0

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