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A priori estimate for maximum modulus of generalized solutions of quasi-linear elliptic equations

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Abstract

Let G be a bounded domain in E n.Consider the following quasi-linear elliptic equation

Although the boundedness of generalized solutions of the equation is proved for very general structural conditions, it does not supply a priori estimate for maximum modulus of solutions. In this paper an estimate to the maximum modulus is made firstly for a special case of quasi-linear elliptic equations, i.e. the \(\overrightarrow A \) and B satisfy the following structural conditions:

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References

  1. Ladyzhenskaya, O.A. and N.N. Ural'ceva,Linear and Quasilinear Elliptic Equations, Academic Press, Beijing (1987). (Chinese version)

    Google Scholar 

  2. Gilbarg, D. and N.S. Trudinger,Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin Heidelberg New York (1977).

    Google Scholar 

  3. Liang Xi-ting, The generalized solutions of one class of elliptic equations,J. Engineering Math.,3, 1 (1986), 19–28. (in Chinese)

    Google Scholar 

  4. Zhu Xi-ping and Yan Jian-fu, Regularity for quasilinear elliptic equations involving critical Sobolev exponent,J. of Systems Sci. and Math. Sci.,9, 1 (1989), 47–52. (in Chinese)

    Google Scholar 

  5. Liang Xi-ting, Boundedness for generalized solutions of quasi-linear elliptic equations,Yinshan Acad. J., 1 (1989), 1–14. (in Chinses)

    Google Scholar 

  6. Miranda, C., Alcune osservazioni Sulla maggiorazione inL r delle soluzioni deboli delle equationi ellittiche del secondo ordine,Ann. Mat. Pura e Appl. 61, 3 (1963), 151–169.

    Google Scholar 

  7. Yu Ming-qi and Liang Xi-ting, The estimate of the maximum modulus for the generalized solutions of elliptic and parabolic equations of second order,J. Shanxi Univ. (Natural Sci. Ed.), 2 (1985), 3–16. (in Chinsese)

    Google Scholar 

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Authors and Affiliations

  1. Zhongshan University, Guangzhou

    Liang Xi-ting

  2. Xuchang Teachers College, Xuchang, Henan

    Wang Xiang-dong

Authors
  1. Liang Xi-ting
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  2. Wang Xiang-dong
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Communicated by Zhang Shi-sheng

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Xi-ting, L., Xiang-dong, W. A priori estimate for maximum modulus of generalized solutions of quasi-linear elliptic equations. Appl Math Mech 11, 941–953 (1990). https://doi.org/10.1007/BF02115678

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  • DOI: https://doi.org/10.1007/BF02115678

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