Skip to main content
Log in

Regularity in elliptic free boundary problems I

  • Published:
Journal d’Analyse Mathématique Aims and scope

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. S. Agmon, A. Douglis and L. Nirenberg,Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, II, Comm. Pure Appl. Math.12 (1959), 623–727;17 (1964), 35–92.

    Article  MATH  MathSciNet  Google Scholar 

  2. N. Aronszajn,A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J. Math. Pures Appl.36 (1957), 235–249.

    MathSciNet  MATH  Google Scholar 

  3. H. Brézis and D. Kinderlehrer,The smoothness of solutions of nonlinear variational inequalities, Indiana Univ. Math. J.23 (1973), 831–844.

    Article  MathSciNet  Google Scholar 

  4. L. A. Caffarelli,The regularity of free boundaries in higher dimensions, Acta Math.139 (1977), 155–184.

    Article  MathSciNet  Google Scholar 

  5. P. Garabedian and M. Schiffer,Variational problems in the theory of elliptic partial differential equations, J. Rat. Mech. Anal.2 (1953), 137–171.

    MathSciNet  Google Scholar 

  6. D. Kinderlehrer,Variational inequalities and free boundary problems, Bull. Amer. Math. Soc.84 (1978), 7–26.

    Article  MATH  MathSciNet  Google Scholar 

  7. D. Kinderlehrer and L. Nirenberg,Regularity in free boundary value problems, Ann. Scuola Norm. Sup. Pisa, Ser. IV,4 (1977), 373–391.

    MATH  MathSciNet  Google Scholar 

  8. D. Kinderlehrer, L. Nirenberg and J. Spruck,Regularité dans les problèmes elliptiques à frontière libre, to appear in C. R. Acad. Sci.

  9. D. Kinderlehrer and J. Spruck,The shape and smoothness of stable plasma configurations, Ann. Scuola Norm. Sup. Pisa. Ser. IV,5 (1978), 131–148.

    MATH  MathSciNet  Google Scholar 

  10. H. Lewy,On the reflection laws of second order differential equations in two independent variables, Bull. Amer. Math. Soc.65 (1959), 37–58.

    MATH  MathSciNet  Google Scholar 

  11. C. B. Morrey, Jr.,Multiple Integrals in the Calculus of Variations, Springer-Verlag, New York-Berlin, 1966.

    MATH  Google Scholar 

  12. J. C. C. Nitsche,The higher regularity of liquid edges in aggregates of minimal surfaces, Nachr. Akad. Wiss. Göttingen Math.-Phys Kl. II, (1977), 75–95.

    Google Scholar 

  13. J. Taylor,The stucture of singularities in soap-bubble-like and soap-film-like minimal surfaces, Ann. of Math.103 (1976), 489–539.

    Article  MathSciNet  Google Scholar 

  14. G. Vergara-Caffarelli,Regolarità di un Problema di Disequazioni Relativo a Due Membrane, Rend. Acad. Lincei50 (1971), 659–662.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

In memory of Nestor Rivière

The first author was partially supported by National Science Foundation grant MPS-75-06489. The second was partially supported by an NSF grant MCS 76-07039 and by a grant from the Office of Naval Research, N00014-76-C-0439. The third was partially supported by NSF grant MPS 75-06490 and by a Sloan Foundation Grant to the Courant Institute.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kinderlehrer, D., Nirenberg, L. & Spruck, J. Regularity in elliptic free boundary problems I. J. Anal. Math. 34, 86–119 (1978). https://doi.org/10.1007/BF02790009

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02790009

Keywords

Navigation