Classical solutions of oblique derivative problem in nonsmooth domains with mean Dini coefficients
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- by Hongjie Dong and Zongyuan Li PDF
- Trans. Amer. Math. Soc. 373 (2020), 4975-4997 Request permission
Abstract:
We consider second-order elliptic equations in nondivergence form with oblique derivative boundary conditions. We show that any strong solutions to such problems are twice continuously differentiable up to the boundary when the boundary can be locally represented by a $C^1$ function whose first derivatives are Dini continuous and the mean oscillations of coefficients satisfy the Dini condition. This improves a recent result by Dong, Lee, and Kim. To the best of our knowledge, such a result is new even for the Poisson equation. An extension to concave fully nonlinear elliptic equations is also presented.References
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Additional Information
- Hongjie Dong
- Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02906
- MR Author ID: 761067
- ORCID: 0000-0003-2258-3537
- Email: hongjie_dong@brown.edu
- Zongyuan Li
- Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02906
- ORCID: 0000-0002-6037-4261
- Email: zongyuan_li@brown.edu
- Received by editor(s): April 12, 2019
- Received by editor(s) in revised form: September 11, 2019, and November 6, 2019
- Published electronically: March 31, 2020
- Additional Notes: The authors were partially supported by the NSF under agreement DMS-1600593.
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 4975-4997
- MSC (2010): Primary 35J25, 35B65; Secondary 35J15
- DOI: https://doi.org/10.1090/tran/8042
- MathSciNet review: 4127868