Skip to main content
Log in

The boundary Harnack principle for linear degenerate elliptic equations in Hölder domains

  • Published:
Proceedings - Mathematical Sciences Aims and scope Submit manuscript

Abstract

In this paper, we establish the boundary Harnack principle for solutions to linear degenerate elliptic equations in Hölder 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. Ancona A, Pricipe de Harnack á la frontième de Fatou pour un opérateur elliptique dans un domaine lipschitzien, Ann. Inst. Fourier (Grenoble) 28 (1978) 169–213

  2. Ba\(\grave{\rm n}\)uelos R, Bass R and Burdzy K, Hölder domain and the boundary Harnack priciple, Duke Math. J. 64 (1991) 195–200

    Article  MathSciNet  Google Scholar 

  3. Bass R and Burdzy K, A boundary Harnack principle in twisted Hölder domains, Ann Math. 134 (1991) 253–276

    Article  MathSciNet  Google Scholar 

  4. Bass R and Burdzy K, The boundary Harnack principle for non-divergence form elliptic operators, J. London Math. Soc. 50 (1994) 157–169

    Article  MathSciNet  Google Scholar 

  5. Bass R and Burdzy K, Lifetimes of conditioned diffusions, Probab. Theory Relat. Fields 91 (1992) 405–443

    Article  MathSciNet  Google Scholar 

  6. Caffarelli L, Fabes E, Mortola S and Salsa S, Boundary behavior of non-negative solutions of elliptic operators in divergence form, Indiana Math. J. 30 (1981) 621–640

    Article  Google Scholar 

  7. Dahlberg E, Estimates of harmonic measure, Arch. Rat. Mech. Anal. 65 (1977) 275–288

    Article  MathSciNet  Google Scholar 

  8. Fabes E, Kenig C and Serapioni R, The local regularity of solutions to degenerate elliptic equations, Comm. Partial Differential Equations 7 (1982) 77–116

    Article  MathSciNet  Google Scholar 

  9. Ferrari F, On boundary behavior of harmonic functions in Hölder domains, J. Fourier Anal. Appl. 4 (1998) 447–461

    Article  MathSciNet  Google Scholar 

  10. Gótmark E and Nystróm K, Boundary behavior of non-negative solutions to degenerate sub-elliptic equations, J. Differential Equations 254 (2013) 3431–3460

    Article  MathSciNet  Google Scholar 

  11. Heinonen J, Kilpelainen T and Martio O, Nonlinear Potential Theory of Degenerate Elliptic Equations (1993) (Oxford: Oxford University Press)

  12. Jerison Fabes D and Kenig C, The winer test for degenerate elliptic equations, Ann. Inst. Fourier (Grenoble) 32 (1982) 151–182

    Article  MathSciNet  Google Scholar 

  13. Jerison Fabes D and Kenig C, Boundary behavior of solutions to degenerate elliptic equations, in: Conference on Harmonic Analysis in Honor of Antonio Zygmund, volumes I, II, Chicago, II (1981) in: Wadsworth MathSer. (1983) (CA: Wadsworth Belmont) pp. 577–589

  14. Jerison D and Kenig C, Boundary behavior of harmonic functions in nontangentially accessible domains, Adv. Math. 46 (1982) 80–147

    Article  MathSciNet  Google Scholar 

  15. Stein E M, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals (1993) (Princeton, NJ: Princeton Univ. Press)

Download references

Acknowledgements

The project was supported by the NNSF(11771023) of China.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lin Tang.

Additional information

Communicated by K Sandeep.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tang, L. The boundary Harnack principle for linear degenerate elliptic equations in Hölder domains. Proc Math Sci 131, 43 (2021). https://doi.org/10.1007/s12044-021-00642-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12044-021-00642-7

Keywords

2000 Mathematics Subject Classification

Navigation