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The Neumann Problem for Parabolic Hessian Quotient Equations

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Abstract

In this paper, we consider the Neumann problem for parabolic Hessian quotient equations. We show that the k-admissible solution of the parabolic Hessian quotient equation exists for all time and converges to the smooth solution of elliptic Hessian quotient equations. Also solutions of the classical Neumann problem converge to a translating solution.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, P. R. China

    Chuan Qiang Chen

  2. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, P. R. China

    Xi Nan Ma

  3. Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, 200433, P. R. China

    De Kai Zhang

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  1. Chuan Qiang Chen
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  2. Xi Nan Ma
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  3. De Kai Zhang
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Correspondence to Chuan Qiang Chen.

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Supported by NSFC (Grant Nos. 11771396, 11721101, 11871255 and 11901102) and China Postdoctoral Science Foundation (Grant No. 2019M651333)

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Chen, C.Q., Ma, X.N. & Zhang, D.K. The Neumann Problem for Parabolic Hessian Quotient Equations. Acta. Math. Sin.-English Ser. 37, 1313–1348 (2021). https://doi.org/10.1007/s10114-021-0340-7

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  • DOI: https://doi.org/10.1007/s10114-021-0340-7

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