Skip to main content
Log in

An ill-posed moving boundary problem for doubly-connected domains

  • Published:
Arkiv för Matematik

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

Access this article

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

Instant access to the full article PDF.

References

  1. Caffarelli, L. A., Compactness methods in free boundary problems,Comm. Partial Differ. Equations,5 (1980), 427–448.

    Article  MATH  MathSciNet  Google Scholar 

  2. Caffarelli, L. A., A remark on the Hausdorff measure of a free boundary, and the convergence of coincidence sets,Boll. Un. Math. Ital. A (5)18 (1981), 109–113.

    MATH  MathSciNet  Google Scholar 

  3. Deny, J., Systèmes totaux de fonctions harmoniques,Ann. Inst. Fourier 1 (1949), 103–113.

    MathSciNet  Google Scholar 

  4. Elliott, C. M., On a variational inequality formulation of an electrochemical machining moving boundary problem and its approximation by the finite element method,J. Inst. Math. Appl. 25 (1980), 121–131.

    Article  MATH  MathSciNet  Google Scholar 

  5. Elliott, C. M. andOckendon, J. R.,Weak and variational methods for moving boundary problems, Pitman, London 1982.

    MATH  Google Scholar 

  6. Fitz-Gerald, J. M. andMcGeough, J. A., Mathematical theory of electrochemical machining, 1. Anodic smoothing,J. Inst. Math. Appl. 5 (1969), 387–408.

    Article  MATH  Google Scholar 

  7. Friedman, A.,Variational principles and free-boundary problems, Wiley, New York 1982.

    MATH  Google Scholar 

  8. Gustafsson, B., Quadrature identities and the Schottky double,Acta Appl. Math. 1 (1983), 209–240.

    Article  MATH  MathSciNet  Google Scholar 

  9. Gustafsson, B., Existence of weak backward solutions to a generalized Hele Shaw flow moving boundary problem,Nonlinear Anal., Theory Methods Appl. 9 (1985), 203–215.

    Article  MATH  MathSciNet  Google Scholar 

  10. Hedberg, L. I., Approximation in the mean by solutions of elliptic equations,Duke Math. J. 40 (1973), 9–16.

    Article  MATH  MathSciNet  Google Scholar 

  11. Keldys, M. V., On the stability of the Dirichlet problem,Uspehi Mat. Nauk 8 (1941), 171–231 (in Russian), translated in Am. Math. Soc. Translations (2)51 (1966), 1–73.

    MathSciNet  Google Scholar 

  12. Kinderlehrer, D. andNirenberg, L., Regularity in free boundary problems,Ann. Scuola Norm. Sup. Pisa Cl. Sci (4)4 (1977), 373–391.

    MATH  MathSciNet  Google Scholar 

  13. Lamb, H.,Hydrodynamics, Cambridge Univ. Press, London 1932.

    MATH  Google Scholar 

  14. Landkoff, N. S.,Foundations of modern potential theory, Springer-Verlag, New York, 1972.

    Google Scholar 

  15. Mossino, J., Inégalités isoperimétriques en électrolyse,C. R. Acad. Sci. Paris, Sér., I,301 (1985), 869–871.

    MATH  MathSciNet  Google Scholar 

  16. Richardson, S., Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel,J. Fluid Mech. 56 (1972), 609–618.

    Article  MATH  Google Scholar 

  17. Rodrigues, J.-F., Further remarks on the stability of the obstacle problem, Pre-publ. 6/84 C. M. A. F., Lisboa (1984).

    Google Scholar 

  18. Sakai, M.,Quadrature domains, Lecture Notes Math. 934, Springer-Verlag, New York, 1982.

    Book  MATH  Google Scholar 

  19. Schaeffer, D. G., A stability theorem for the obstacle problem,Adv. Math. 16 (1975), 34–47.

    Article  Google Scholar 

  20. Warner, F. W.,Foundation of differentiable manifolds and Lie groups, Scott, Foresman and Company, Glenview, 1971.

    Google Scholar 

  21. Widman, K. O., Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations,Math. Scand. 21 (1967), 17–37.

    MATH  MathSciNet  Google Scholar 

  22. Brezis, H. andKinderlehrer, D., The smoothness of solutions to nonlinear variational inequalities,Indiana Univ. Math. J.23 (1974), 831–844.

    Article  MATH  MathSciNet  Google Scholar 

  23. Frehse, I., On the regularity of the solution of a second order variational inequality,Boll. Un. Mat. Ital. 6 (1972), 312–315.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gustafsson, B. An ill-posed moving boundary problem for doubly-connected domains. Ark. Mat. 25, 231–253 (1987). https://doi.org/10.1007/BF02384446

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02384446

Keywords

Navigation