Skip to main content
Log in

Boundary Hölder Estimates for a Class of Degenerate Elliptic Equations in Piecewise Smooth Domains

  • Published:
Chinese Annals of Mathematics, Series B Aims and scope Submit manuscript

Abstract

In this paper, the authors will apply De Giorgi-Nash-Moser iteration to establish boundary Hölder estimates for a class of degenerate elliptic equations in piecewise C2-smooth domains.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Daskalopoulos, P. and Lee, K.-A., Hölder regularity of solutions of degenerate elliptic and parabolic equations, Journal of Functional Analysis, 201(2) 2003, 341–379.

    Article  MATH  MathSciNet  Google Scholar 

  2. De Giorgi, E., Sulla differenziabilità e lanalicità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino cl. Sci. Fis. Fat. Nat., 3, 1957, 25–43.

    MATH  Google Scholar 

  3. Fichera, G., Sulle equazioni differenziali lineari ellittico-paraboliche del secondo ordine, Atti Accad. Naz. Lincei Mem. Ci. Fis. Mat. Natur. Sez. I, 5(8) 1956, 1–30.

    MATH  MathSciNet  Google Scholar 

  4. Fichera, G., On a unified theory of boundary value problems for elliptic-parabolic equations of second order, Matematika, 7(6) 1963, 99–122.

    MATH  Google Scholar 

  5. Gilbarg, D. and Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 2015.

    MATH  Google Scholar 

  6. Han, Q., Hong, J. and Huang, G., Compactness of Alexandrov-Nirenberg Surfaces, Communications on Pure and Applied Mathematics, 70(9) 2017, 1706–1753.

    Article  MATH  MathSciNet  Google Scholar 

  7. Huang, G., A priori bounds for a class of semi-linear degenerate elliptic equations, Science China Mathematics, 57(9) 2012, 1911–1926.

    Article  MATH  MathSciNet  Google Scholar 

  8. Keldyš, M. V., On certain cases of degeneration of equations of elliptic type on the boundary of a domain, Dokl. Akad. Nauk SSSR, 77, 1951, 181–183.

    Google Scholar 

  9. Morrey, C. B., On the solutions of quasi-linear elliptic partial differential equations, Transactions of the American Mathematical Society, 43(1) 1938, 126–166.

    Article  MATH  MathSciNet  Google Scholar 

  10. Nash, J., Continuity of solutions of parabolic and elliptic equations, Amer. J. Math., 80, 1958, 931–954.

    Article  MATH  MathSciNet  Google Scholar 

  11. Oleǐnik, O. A., A problem of Fichera, Dokl. Akad. Nauk SSSR, 157, 1964, 1297–1300.

    MATH  MathSciNet  Google Scholar 

  12. Oleǐnik, O. A., Linear equations of second order with nonnegative characteristic form, Mat. Sb., 69(111) 1966, 111–140.

    MathSciNet  Google Scholar 

  13. Oleǐnik, O. A. and Radkevič, E. V., Second Order Equations with Nonnegative Characteristic Form, Amer. Math. Soc., RI/Plenum Press, New York, 1973.

    Book  Google Scholar 

  14. Weber, B., Regularity and a Liouville theorem for a class of boundary-degenerate second order equations, Journal of Differential Equations, 281, 2021, 459–502.

    Article  MATH  MathSciNet  Google Scholar 

  15. Zhang, F. and Du, K., Krylov-Safonov estimates for a degenerate diffusion process, Stochastic Processes and their Applications, 130(8) 2020, 5100–5123.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Jiaxing Hong or Genggeng Huang.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11631011, 11871160, 12141105).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hong, J., Huang, G. Boundary Hölder Estimates for a Class of Degenerate Elliptic Equations in Piecewise Smooth Domains. Chin. Ann. Math. Ser. B 43, 719–738 (2022). https://doi.org/10.1007/s11401-022-0354-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11401-022-0354-1

Keywords

2000 MR Subject Classification

Navigation