Skip to main content

Some Remarks on Dirichlet Problem

  • Chapter
  • 182 Accesses

Abstract

In the theory of harmonic spaces (see [1], [3]) the Laplace and the heat equations can be investigated simultaneously. We shall do some remarks on boundary value problems from this abstract point of view.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Bauer, Harmonische Räume und ihre Potentialtheorie, Lecture Notes in Math. 22, Berlin 1966

    Google Scholar 

  2. Ju.D. Burago, V.G. Mazja, V.P. Sapožnikova, K teorii potencialov dvojnogo i prostogo sloja dlja oblastej s nereguljarnymi granicami, Sbornik Problemy mat. Ana’iza, Krajevyje zadaci i integralnyje uravnenija, Leningrad 1966

    Google Scholar 

  3. C. Constantinescu, A. Cornea, Potenzial Theory on Harmonie Spaces, Berlin 1972

    Google Scholar 

  4. E. deGiorgi, Nuovi teoremi relativi alle misure (r - 1)-dimensionali in uno Spazio ad r dimensioni, Ricerche Mat. 4, (1955), 95–113

    MathSciNet  Google Scholar 

  5. M. Dont, Non-tangential limits of the double layer potential, čas. pro pěst. mat. 97, (1972), 231–238

    MathSciNet  MATH  Google Scholar 

  6. H. Federer, The Gauss-Green theorem, TAMS 58, (1945), 44–76

    MathSciNet  MATH  Google Scholar 

  7. R.A. Hunt, R.L. Wheeden, Positive Harmonic Functions on Lipschitz Domains, TAMS 147, (1970), 507–527

    Article  MathSciNet  MATH  Google Scholar 

  8. J.T. Kemper, Temperatures in Several Variables: Kernel Functions, Representations, and Parabolic Boundary Values TAMS 167, (1972), 243–262

    MathSciNet  MATH  Google Scholar 

  9. J. Krái, The Fredholm radius of an operator in potential theory I, II, Czech. Mat. J. 15 (90), 1965, 454–473, 565–588

    Google Scholar 

  10. J. Krái, The Fredholm Method in Potential Theory TAMS 125 (1966), 511–547

    Google Scholar 

  11. J. Krái, Flows of heat and the Fourier problem, Czech. Mat. J. 20 (95), 1970, 556–598

    Google Scholar 

  12. I. Netuka, The third boundary value problem in potential theory, Czech. Mat. J. 22 (1972), 554–580

    MathSciNet  Google Scholar 

  13. J. Veselý, On the heat potential of the double distribution, Čas. pro pěst, mat. 98 (1973), 181–198

    MATH  Google Scholar 

  14. J. Veselý, Úhlové limity potenciálů dvojvrstvy (English summary), Čas. pro pěst. mat. 95 (1970), 379–401

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Academia, Publishing House of the Czechoslovak Academy of Sciences

About this chapter

Cite this chapter

Veselý, J. (1975). Some Remarks on Dirichlet Problem. In: Král, J. (eds) Nonlinear Evolution Equations and Potential Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-4425-4_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-4425-4_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-4427-8

  • Online ISBN: 978-1-4613-4425-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics