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Applied Mathematics and Mechanics

, Volume 15, Issue 11, pp 1025–1034 | Cite as

A priori estimates to the maximum modulus of generalized solutions of a class of quasilinear elliptic equations with anisotropic growth conditions

  • Liang Xi-ting
  • Wang Xiang-dong
Article
  • 20 Downloads

Abstract

In this paper we give a priori estimates for the maximum modulus of generalized solutions of the quasilinear elliptic equations with anisotropic growth condition.

Keywords

quasilinear elliptic equation nonstandard growth condition anisotropic Sobolev space generalized solution maximum modulus a priori estimate 

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References

  1. [1]
    Lu Wen-duan. The Dirichlet problem for a class of quasilinear elliptic equations of second order.Advances in Math.,14 (1985), 276–278.Google Scholar
  2. [2]
    Lu Wen-duan. The Dirichlet problem for a class of nonlinear elliptic equation.J. Math. Research Exposition,6 (1986), 51–56.Google Scholar
  3. [3]
    Chen Zu-chi and Shen Yao-tian. Nontrivial solutions of the Dirichlet problem for a class of nonlinear elliptic equation.Acta Math. Sci.,7 (1987), 63–74.Google Scholar
  4. [4]
    Lu Wen-duan. Global boundedness for weak solutions of sencond order quasilinear elliptic equations in divergence from.J. Part. Diff. Equ., Ser. B1, 2 (1988), 12–16 (in Chinese)Google Scholar
  5. [5]
    Wang Xiang-dong and Liang Xi-ting. The boundedness for generalized solutions of a class of elliptic equations.J. Huaihua Teachers College,9 (1990), 89–96. (in Chinese)Google Scholar
  6. [6]
    Wang Xiang-dong and Liang Xi-ting. The local boundedness for-solutions of quasilinear elliptic equations in anisotropic Sobolev space,J. Applied Mathematics.Google Scholar
  7. [7]
    Fusco, N. and C. Sbordone, Local boundedness of minimizers in a limited case. Manuscripts Math.,69 (1990), 19–25.zbMATHMathSciNetGoogle Scholar
  8. [8]
    Liang Xi-ting, Boundedness of minimizers of functionals involving critical growth exponent,Trans. Amer. Math. Soc..Google Scholar
  9. [9]
    Ladyzenskaja, O. A. and N. N. Ural’ceva. Linear and quasilinear equations of elliptic type. Nauka, Moscow (1973). Chinese Transl., Academic Press, Beijing, (1987).Google Scholar
  10. [10]
    Liang Xi-ting and Wang Xiang-dong, A priori estimate for maximum modulus of generalized solutions of quasilinear elliptic equations.Appl. Math. and Mech. (English Fd.),11, 10 (1990), 941–953.MathSciNetCrossRefGoogle Scholar

Copyright information

© SUT 1994

Authors and Affiliations

  • Liang Xi-ting
    • 1
  • Wang Xiang-dong
    • 2
  1. 1.Department of MathematicsZhongshan UniversityGuangzhou
  2. 2.Department of MathamaticsXuchang Teachers CollegeZhengzhou

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