Skip to main content

Monotone Dirichlet forms and resolvents

  • Chapter
ICPT ’91
  • 113 Accesses

Abstract

We define a nonlinear Dirichlet form associated with a monotone operator. Using the Monge-Ampère operator as an example, we prove potential theoretic properties of such a form and introduce an associated resolvent.

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
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. T. Aubin. Nonlinear Analysis on Manifolds. Monge-Ampère Equations, Springer-Verlag, 1982.

    Book  Google Scholar 

  2. L.J. Bakelman. Generalized Elliptic Solutions of the Dirichlet Problem for n-dimensional Monge-Ampère Equations. Proceedings of Symposia in Pure Mathematics, 45,1:73–102, 1986.

    MathSciNet  Google Scholar 

  3. E.M.J. Bertin. Equation de Monge-Ampère et théorie du Potentiel. L’axiome de faisceau. Preprint 25, Utrecht, 1976.

    Google Scholar 

  4. N. Bourbaki. Intégration, chapitre IX, Hermann, 1969.

    Google Scholar 

  5. B. Calvert. Potential theoretic properties for Monotone Operators. Boll. Un. Mat. Ital. (4), 5:473–489, 1972.

    MathSciNet  MATH  Google Scholar 

  6. J. Deny. Méthodes Hilbertiennes et théorie du potentiel. Potential theory, C.I.M.E., Edizioni Cremonese, 1970.

    Google Scholar 

  7. H. Jeggle. Nichtlineare Funktionalanalysis. B.G. Teubner, 1979.

    MATH  Google Scholar 

  8. M. Fukushima. Dirichlet Forms and Markov Processes. North-Holland, 1980.

    MATH  Google Scholar 

  9. N. Kenmochi and Y. Mizuta. The gradient of a convex function on a regular functional space and its potential theoretic properties. Hiroshima Math. J., 4:743–763, 1974.

    MathSciNet  MATH  Google Scholar 

  10. N. Kenmochi and Y. Mizuta. Potential theoretic properties of the gradient of a convex function on a functional space. Nagoya Math. J., 59:199–215, 1975.

    MathSciNet  MATH  Google Scholar 

  11. Y. Mizuta and T. Nagai. Potential theoretic properties of the Subdifferential of a Convex Function. Hiroshima Math. J., 7:177–182, 1977.

    MathSciNet  MATH  Google Scholar 

  12. J. Rauch and B.A. Taylor. The Dirichlet Problem for the multidimensional Monge-Ampère Equation. Rocky Mountain J. Math., 7:345–363, 1977.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

van Beusekom, P. (1994). Monotone Dirichlet forms and resolvents. In: Bertin, E. (eds) ICPT ’91. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1118-8_13

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-1118-8_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4488-2

  • Online ISBN: 978-94-011-1118-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics