Skip to main content

Inequalities Between Normal And Tangential Derivatives Of Harmonic Functions

  • Chapter
  • First Online:
Unpublished Manuscripts
  • 1786 Accesses

Abstract

For functions which are harmonic in a sphere, Višik [9] has proved an estimate of the normal derivative in terms of the tangential ones.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • 1. V. G. Avakumovič Über die Eigenfunktionen auf geschlossenen Riemannschen Manningfaltigkeiten, Math. Z. 65 (1956), 327–344.

    Google Scholar 

  • 2. K. Friedrichs and H. Lewy, Über die Eindeutigkeit und das Abhängigkeitsgebiet der Lӧsungen beim Anfangswertproblem linearer hyperbolischer Differentiagleichungen, Math. Ann. 98 (1928), 299–326.

    Google Scholar 

  • 3. L. Hӧrmander, uniqueness theorems and estimates for normally hyperbolic partial differential equations of the second order, C.R. 12e Congr. Math. Scand. Lund (1953), 105–115.

    Google Scholar 

  • 4. B. M. Lewitan, On the asymptotic behavior of the spectral function and on expansion in eigenfunctions of a self-adjoint differential equation of second order II, Izv. Akad. Nauk SSSR Ser. Mat. 19 (1955), 33–58.

    Google Scholar 

  • 5. S. G. Mihlin, On an inequality for the boundary values of harmonic functions, Uspehi Matem. Nauk 6:6 (1951), 158–159, (Russian).

    Google Scholar 

  • 7. L. E. Payne and H. F. Weinberger, New bounds in harmonic and biharmonic problems, J. of Math. and physics 33 (1955), 291–307.

    Google Scholar 

  • 8. L. Sandgren, A vibration problem, Comm. Sém. Math. Univ. Lund 19 (1955), 1–84.

    Google Scholar 

  • 9. M. I. Višik, On an inequality for the boundary values of harmonic functions in a sphere, Uspehi Matem. Nauk 6:2 (1951), 165–166, (Russian).

    Google Scholar 

  • 10. M. I. Višik, On general boundary Problems for elliptic differential equations, Trudy Moskov. Mat. Obšč. 1 (1952), 187–246, (Russian).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lars Hörmander .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Hörmander, L. (2018). Inequalities Between Normal And Tangential Derivatives Of Harmonic Functions. In: Unpublished Manuscripts . Springer, Cham. https://doi.org/10.1007/978-3-319-69850-2_6

Download citation

Publish with us

Policies and ethics