Skip to main content
SpringerLink
Log in

On the obstacle problem with a volume constraint

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

We show that the solutions u∈K of

$$\mathop \smallint \limits_\Omega \nabla u\nabla (u - v)dx \leqq 0forallv\varepsilon K$$

where

are of class Co,α (Ω) or Co,α (Ω), if the obstacles have this property. The same fact is true for systems of variational inequalities with constant coefficients, when there are no obstacles.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. KINDERLEHRER, D., STAMPACCHIA, G.: An Introduction to Variational Inequalities and Their Applications. Academic Press, New York 1980.

    Google Scholar 

  2. HILDEBRANDT, S., WENTE, H.: Variational Problems with Obstacles and a Volume Constraint. Math. Zeitschrift135, 55–68 (1973).

    Google Scholar 

  3. HILDEBRANDT, S., MEIER, M.: On Variational Problems with Obstacles and Integral Constraints for Vector-Valued Functions. Man. math.28, 185–206 (1979).

    Google Scholar 

  4. EISEN, G.: Ober die Regularität schwacher Lösungen von Variationsproblemen mit Hindernissen und Integralbedingungen. Preprint No. 512, Sonderforschungsbereich 72, Bonn 1982 (Thesis).

  5. CAMPANATO, S.: Equazioni ellitiche del secondo ordine e spaziL 2,λ. Annali Mat. Pura Appl.69, 321–381 (1965).

    Google Scholar 

  6. MORREY, C.B.: Multiple Integrals in the Calculus of Variations. Springer, New York 1966.

    Google Scholar 

  7. GIAQUINTA, M.: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. Vorlesungsreihe SFB 72 No. 6, Bonn 1981.

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut, Universität Bonn, Beringstr. 4, 5300, Bonn 1, BRD

    Goswin Eisen

Authors
  1. Goswin Eisen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eisen, G. On the obstacle problem with a volume constraint. Manuscripta Math 43, 73–83 (1983). https://doi.org/10.1007/BF01169097

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01169097

Keywords

Search

Navigation