Abstract
In this paper, a new method is represented to investigate boundary \(W^{2,p}\) estimates for elliptic equations, which is, roughly speaking, to derive boundary \(W^{2,p}\) estimates from interior \(W^{2,p}\) estimates by Whitney decomposition. Using it, \(W^{2,p}\) estimates on \(C^{1,\alpha }\) domains are obtained for nondivergence form linear elliptic equations and further more, fully nonlinear elliptic equations are also considered.
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Acknowledgements
The first author is supported by National Science Foundation of China: Grant no. 12071365. The third author is supported by China Postdoctoral Science Foundation: Grant no. 2022M712081 and by the Institute of Modern Analysis-A Frontier Research Center of Shanghai.
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Li, D., Li, X. & Zhang, K. \(\varvec{{W}^{2,p}}\) Estimates for elliptic equations on \(\varvec{C^{1,\alpha }}\) domains. Math. Ann. 387, 57–78 (2023). https://doi.org/10.1007/s00208-022-02448-y
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DOI: https://doi.org/10.1007/s00208-022-02448-y