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Singularities of Solutions of a Class of Quasilinear Equations in Divergence Form

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Nonlinear Diffusion Equations and Their Equilibrium States, 3

Abstract

In Section 1 of this paper we study the behavior near the origin of the positive nonradial solutions of the doubly nonlinear N-dimensional partial differential equation

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References

  1. Ph. Benilan, personnal communication (1988).

    Google Scholar 

  2. Ph. Benilan, H. Brezis and M.G. Crandall, A semilinear elliptic equation in L1(ℝ n, Ann. Scuola Norm Sup. Pisa, 2(1975), 523–555.

    MathSciNet  MATH  Google Scholar 

  3. M.F. Bidaut-Veron, Local and global behavior of solutions of quasilinear equations of Emden-Fowler type, Arch, for Rat. Mech. Anal. 107(4) (1989), 293–324.

    Article  MathSciNet  MATH  Google Scholar 

  4. H. Brezis and P.L. Lions, A note on isolated singularities for linear elliptic equations, Jl. Math. Anal, and Appl. 7A(1981), 263–266.

    MathSciNet  Google Scholar 

  5. A. Friedman and L. Veron, Singular solutions of some quasilinear elliptic equations, Arch, for Rat. Mech. Anal. 96(1986), 259–287.

    MathSciNet  Google Scholar 

  6. M. Guedda and L. Veron, Local and global properties of solutions of quasilinear equations, Jl. Diff. Eq. 76(1988), 159–189.

    Article  MathSciNet  MATH  Google Scholar 

  7. S. Kichenassamy and L. Veron, Singular solutions of the p-Laplace equation, Math. Ann. 275(1986), 599–615.

    Article  MathSciNet  MATH  Google Scholar 

  8. P.L. Lions, Isolated singularities in semilinear problems, Jl. Diff. Eq. 38(1980), 441–450.

    Article  MATH  Google Scholar 

  9. W.M. Ni and J. Serrin, Existence and nonexistence theorems for ground states of quasilinear partial differential equations: the anomalous case, Acad. Naz. dei. Lincei 77(1986), 231–257.

    Google Scholar 

  10. P. Pucci and J. Serrin, Continuation and limit properties for solutions of strongly nonlinear second order differential equations, to appear.

    Google Scholar 

  11. J. Serrin, Local behavior of solutions of quasilinear equations, Acta Math., 111(1964), 247–302.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Serrin, Isolated singularities of solutions of quasilinear equations, Acta Math. 113(1965), 219–240.

    Article  MathSciNet  MATH  Google Scholar 

  13. P. Tolksdorff, On the Dirichlet problem for quasilinear equations in domains with conical boundary points, Comm. in Part. Diff. Eq. 8(7) (1983), 773–817.

    Article  Google Scholar 

  14. P. Tolksdorff, Regularity for a more general class of quasilinear elliptic equations, Jl. Diff. Eq. 51(1984), 126–150.

    Article  Google Scholar 

  15. N.S. Trudinger, On Harnack type inequalities and their applications to quasi-linear elliptic equations, Comm. in Pure and Appl. Math. 20(1967), 721–747.

    Article  MathSciNet  MATH  Google Scholar 

  16. J.L. Vazquez, A strong maximum principle for some quasilinear elliptic equations, Appl. Math. Opt. 12(1984), 191–202.

    Article  MATH  Google Scholar 

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© 1992 Springer Science+Business Media New York

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Bidaut-Veron, MF. (1992). Singularities of Solutions of a Class of Quasilinear Equations in Divergence Form. In: Lloyd, N.G., Ni, W.M., Peletier, L.A., Serrin, J. (eds) Nonlinear Diffusion Equations and Their Equilibrium States, 3. Progress in Nonlinear Differential Equations and Their Applications, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0393-3_9

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  • DOI: https://doi.org/10.1007/978-1-4612-0393-3_9

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6741-6

  • Online ISBN: 978-1-4612-0393-3

  • eBook Packages: Springer Book Archive

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