Skip to main content

Regularity of the extremal solutions for the Liouville system

  • Conference paper
Geometric Partial Differential Equations proceedings

Part of the book series: CRM Series ((CRMSNS,volume 15))

Abstract

We study the smoothness of the extremal solutions to the Liouville system.

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

Access this chapter

eBook
USD 24.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 34.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. C. Cowan, Regularity of the extremal solutions in a Gelfand systems problem, Advanced Nonlinear Studies 11 (2011), n. 3, 695–700.

    MATH  MathSciNet  Google Scholar 

  2. C. Cowan and N. Ghoussoub, Regularity of semi-stable solutions to fourth order nonlinear eigenvalue problems on general domains, Calc. Var., to appear.

    Google Scholar 

  3. L. Dupaigne, “Stable Solutions of Elliptic Partial Differential Equations”, Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, Vol. 143, Chapman & Hall/CRC, Boca Raton, FL, 2011, xiv+321.

    Google Scholar 

  4. L. Dpaigne, M. Ghergu, O. Goubet and G. Warnault, The Gel’fand problem for the biharmonic operator, Arch. Ration. Mech. Anal. 208 (2013), n. 3, 725–752.

    Article  MathSciNet  Google Scholar 

  5. P. Esposito, N. Ghoussoub and Y. Guo, “Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS”, Courant Lecture Notes in Mathematics, Vol. 20, Courant Institute of Mathematical Sciences, New York, 2010, xiv+318.

    Google Scholar 

  6. M. Montenegro, Minimal solutions for a class of elliptic systems, Bull. London Math. Soc. 37 (2005), 405–416.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Scuola Normale Superiore Pisa

About this paper

Cite this paper

Dupaigne, L., Farina, A., Sirakov, B. (2013). Regularity of the extremal solutions for the Liouville system. In: Chambolle, A., Novaga, M., Valdinoci, E. (eds) Geometric Partial Differential Equations proceedings. CRM Series, vol 15. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-473-1_7

Download citation

Publish with us

Policies and ethics