Skip to main content
Log in

Integral Representations for Solutions of Some Types of the Beltrami Equations

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We obtain integral representations for solutions of some types of the Beltrami equations. These representations allow us to prove analogs of some classical complex analysis for these solutions.

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. Vekua, I. N. Generalized Analytic Functions (Nauka, Moscow, 1988) [in Russian].

    MATH  Google Scholar 

  2. Bojarski, B. “Old and New on Beltrami Equations”, Functional analytic methods in complex anal. and appl. to partial diff. equat., Proc. of ICTP, 8–19 (1988).

  3. Iwaniec, T. and Martin, G. “What’s New for the Beltrami Equation”? Geometric Anal. and Appl. Proc. Centre Math. Appl. Australian Nation. Univ., Canberra 39, 132–148 (2001).

    MathSciNet  MATH  Google Scholar 

  4. Tungatarov, A. B. “On Properties of Certain Integral Operator in Classes of Summable Functions”, Izv. AN Kaz. SSR. Ser. Fiz.-Mat,No. 5, 58–62 (1985) [in Russian].

    MATH  Google Scholar 

  5. Abreu-Blaya, R., Bory-Reyes, J. and Pen˜a-Pen D. “On the Jump Problem for β-Analytic Functions”, Complex Var. and Elliptic Equat. 51, No. 8–11, 763–775 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  6. Abreu Blaya, R., Bory Reyes, J., Pen˜a-Pen˜a, D., Vilaire, J.-M. “Riemann Boundary Value Problem for β-Analytic Functions”, Internat. J. Pure Appl.Math. 42, No. 1, 19–37 (2008).

    MathSciNet  Google Scholar 

  7. Gakhov, F. D. Boundary Value Problems (Nauka, Moscow, 1977) [in Russian].

    MATH  Google Scholar 

  8. Markushevich, A. I. Selected Chapters of Theory of Analytic Functions (Nauka, Moscow, 1976) [in Russian].

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to D. B. Katz.

Additional information

Original Russian Text © D.B. Katz, B.A. Kats, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 3, pp. 23–28.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Katz, D.B., Kats, B.A. Integral Representations for Solutions of Some Types of the Beltrami Equations. Russ Math. 62, 18–22 (2018). https://doi.org/10.3103/S1066369X18030039

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X18030039

Keywords

Navigation