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Pointwise boundary differentiability for fully nonlinear elliptic equations

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Abstract

In this paper, we prove the pointwise boundary differentiability for viscosity solutions of fully nonlinear elliptic equations. This generalizes the previous related results for linear equations and the geometrical conditions in this paper are pointwise and more general. Moreover, our proofs are relatively simple.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, Shaanxi, 710129, PR China

    Duan Wu

  2. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China

    Yuanyuan Lian & Kai Zhang

Authors
  1. Duan Wu
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  2. Yuanyuan Lian
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  3. Kai Zhang
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Corresponding author

Correspondence to Yuanyuan Lian.

Additional information

This research is supported by the National Natural Science Foundation of China (Grant Nos. 12031012, 11831003 and 12171299) and the China Postdoctoral Science Foundation (Grant Nos. 2021M692086 and 2022M712081).

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Wu, D., Lian, Y. & Zhang, K. Pointwise boundary differentiability for fully nonlinear elliptic equations. Isr. J. Math. 258, 375–401 (2023). https://doi.org/10.1007/s11856-023-2476-x

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  • DOI: https://doi.org/10.1007/s11856-023-2476-x

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