Skip to main content
Log in

Singular solutions of thep-laplace equation

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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.

Institutional subscriptions

References

  1. Dibenedetto, E.:C 1+α local regularity of weak solutions of degenerate elliptic equations. Nonlinear Anal., Theory Methods Appl.7, 827–850 (1983)

    Google Scholar 

  2. Bojarski, B., Iwaniec, T.:p-Harmonic equation and quasilinear mappings. Sonderforschungsbereich 72, Univ. Bonn (1983)

  3. Chrusciel, P.: Sur l'existence de solutions singulières d'une équation «condition de coordonnées» utilisée par J. Kijowski dans l'analyse symplectique de la relativité générale. C. R. Acad. Sci. Paris299I, 891–894 (1984)

    Google Scholar 

  4. Chrusciel, P.: Conformally minimal foliations of three dimensional Riemannian manifolds and the energy of the gravitational field. Ph.D. Thesis, Inst. Th. Phys. Polish Acad. Sci. (1986)

  5. Dobrowolski, M.: Nichtlineare Eckenprobleme und finite Elementenmethode. Z. Angew. Math. Mech.64, 270–271 (1984)

    Google Scholar 

  6. Evans, L.C.: A new proof of localC 1,α regularity for solutions of certain degenerate elliptic P.D.E.. J. Differ. Equations50, 315–338 (1982)

    Google Scholar 

  7. Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Berlin, Heidelberg, New York: Springer 1982

    Google Scholar 

  8. Kichenassamy, S., Veron, L.: Singularités isolées de l'équation 614-1. C.R. Acad. Sci. Paris301, 149–151 (1985)

    Google Scholar 

  9. Krol, I.N.: On the behaviour of the solutions of a quasilinear equation near null salient points of the boundary. Proc. Steklov Inst. Math.125, 130–136 (1973)

    Google Scholar 

  10. Krol, I.N., Mazja, V.G.: The lack of continuity and Hölder continuity of the solutions of a certain quasilinear equation Sem. Math. V. A. Steklov Math. Inst. Leningrad14, 44–45 (1969)

    Google Scholar 

  11. Ladyzhenskaya, O.A., Ural'Ceva, N.N.: Linear and quasilinear elliptic equations. London, New York: Academic Press 1968

    Google Scholar 

  12. Lewis, J.L.: Smoothness of certain degenerate elliptic equations. Proc. AMS80, 259–265 (1980)

    Google Scholar 

  13. Lewis, J.L.: Regularity of the derivatives of solutions to certain degenerate elliptic equations. Indiana Univ. Math. J.32, 849–858 (1983)

    Google Scholar 

  14. Lions, J.L.: Quelques méthodes de résolutions des problèmes aux limites non linéaires. Paris: Dunod-Gauthier-Villars 1969

    Google Scholar 

  15. Reshetniak, Y.G.: Mappings with bounded deformation as extremals of Dirichlet type integrals. Sibirsk. Mat. Zh.9, 652–666 (1966)

    Google Scholar 

  16. Serrin, J.: Local behaviour of solutions of quasilinear equations. Acta Math.111, 247–302 (1964)

    Google Scholar 

  17. Serrin, J.: Isoled singularities of solutions of quasilinear equations. Acta Math.113, 219–240 (1965)

    Google Scholar 

  18. Serrin, J.: Singularities of solutions of nonlinear equations. Proc. Symp. Appl. Math.17, 68–88 (1965)

    Google Scholar 

  19. Tolksdorf, P.: Regularity for a more general class of quasilinear elliptic equations. J. Differ. Equations51, 126–150 (1984)

    Google Scholar 

  20. Tolksdorf, P.: On the Dirichlet problem for quasilinear equations in domain with conical boundary points. Commun. Partial Differ. Equations8, 773–817 (1983)

    Google Scholar 

  21. Uhlenbeck, K.: Regularity for a class of nonlinear elliptic systems. Acta Math.138, 219–240 (1977)

    Google Scholar 

  22. Ural'Ceva, N.N.: Degenerate quasilinear systems. Sem. Math. V.A. Steklov, Math. Inst. Leningrad7, 83–99 (1968)

    Google Scholar 

  23. Véron, L.: Anisotropic singularities of degenerate eliptic equations (in preparation)

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kichenassamy, S., Veron, L. Singular solutions of thep-laplace equation. Math. Ann. 275, 599–615 (1986). https://doi.org/10.1007/BF01459140

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01459140

Keywords

Navigation