Glasnik Matematicki, Vol. 49, No. 2 (2014), 369-375.

ON QUALITATIVE PROPERTIES OF SOLUTIONS OF QUASILINEAR ELLIPTIC EQUATIONS WITH STRONG DEPENDENCE ON THE GRADIENT

Jadranka Kraljević

Department of Mathematics, Faculty of Economics, University of Zagreb, Kennedyev trg 6, 10000 Zagreb, Croatia
e-mail: jkraljevic@efzg.hr


Abstract.   We are interested in the regularity of positive, spherically symmetric solutions of a class of quasilinear elliptic equations involving the p-Laplace operator, with an arbitrary positive growth rate e0 on the gradient on the right-hand side. We study the regularity of a class of strong and weak solutions at the origin. Furthermore, we find some conditions under which strong solutions are classical.

2010 Mathematics Subject Classification.   35C15, 35J60, 45J05.

Key words and phrases.   Quasilinear elliptic, positive strong solution, weak solution, regularity, classical solution.


Full text (PDF) (free access)

DOI: 10.3336/gm.49.2.10


References:

  1. D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin, 1983.
    MathSciNet     CrossRef

  2. L. Horvat, J. Kraljević, D. Žubrinić and V. Županović, Positive solutions of polyharmonic equations with strong dependence on the gradient, Complex Var. Elliptic Equ. 52 (2007), 693-707.
    MathSciNet     CrossRef

  3. L. Korkut, M. Pašić and D. Žubrinić, A singular ODE related to quasilinear elliptic equations, Electron. J. Differential Equations 2000, No. 12, 37 pp.
    MathSciNet    

  4. J. Kraljević, and D. Žubrinić, Quasilinear elliptic equations with positive exponent on the gradient, Glas. Mat. Ser. III 48(68) (2013), 391-402.
    MathSciNet     CrossRef

  5. M. Pašić, Nonexistence of spherically symmetric solutions for p-Laplacian in the ball, C. R. Math. Acad. Sci. Soc. R. Can. 21 (1999), 16-22.
    MathSciNet    

  6. D. Žubrinić, Positive solutions of quasilinear elliptic systems with the natural growth in the gradient, Rend. Istit. Mat. Univ. Trieste 32 (2000), 65-102.
    MathSciNet    

  7. D. Žubrinić, Solvability of quasilinear elliptic equations with strong dependence on the gradient, Abstr. Appl. Anal. 5 (2000), 159-173.
    MathSciNet     CrossRef

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