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On the regularity of solutions of boundary-value problem for quasilinear elliptic systems with quadratic nonlinearity

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The partial regularity up to the boundary of a domain is established for a solution u ∈ H1 (Ω) ∩ L (Ω) to the boundary-value problem for a second-order elliptic system with strong nonlinearity in the case of dimension n≥3. Bibliography: 12 titles.

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Literature Cited

  1. M. Giaquinta,Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. Princeton University Press, Princeton (1983).

    Google Scholar 

  2. F. Colombini, E. De Giorgi, and F. Piccinini. “Frontiere orientate di misure minima e questioni collegate,”Ed. Tecnico Scientifica Sci. Norm. Super. Pisa (1972).

  3. S. Campanato, “Equazioni ellittiche del secondo ordine e spazi L(2,λ),”Ann. Mat. Pura Appl. (4),69, 321–381 (1965).

    MATH  MathSciNet  Google Scholar 

  4. M. Giaquinta, “A counter-example to the boundary regularity of solutions to elliptic quasilinear systems,”Manuscr. Math.,26, 217–220 (1978).

    MathSciNet  Google Scholar 

  5. M. Giaquinta and G. Modica, “Nonlinear systems of the type of the stationary Navier-Stokes systems,”J. Reine Angew. Math.,330, 173–214 (1982).

    MathSciNet  Google Scholar 

  6. A. A. Arkhipova, “Partial regularity of solutions of a quasilinear elliptic system with a nonsmooth condition for a conormal derivative,”Mat. Sb.,184, No. 2, 87–104 (1993).

    MATH  Google Scholar 

  7. A. A. Arkhipova, “On the regularity of solutions of a problem with directorial derivative for quasilinear elliptic systems,”Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov (POMI),213, 5–13 (1994).

    MATH  MathSciNet  Google Scholar 

  8. A. A. Arkhipova, “Regularity results for quasilinear elliptic systems with nonlinear boundary conditions,”Probl. Mat. Anal., No. 14, 23–51 (1995).

    MATH  Google Scholar 

  9. M. Giaquinta and E. Guisti, “Nonlinear elliptic systems with quadratic growth,”Manuscr. Math.,24, No. 3, 323–349 (1978).

    Google Scholar 

  10. P. Cannarsa, “On a maximum principle for elliptic systems with constant coefficients,”Rend. Sem. Mat. Univ. Padova,64, 77–84 (1981).

    MATH  MathSciNet  Google Scholar 

  11. A. A. Arkhipova, “Inverse Hölder inequalities with boundary integral andL p -estimates in problems with Neumann conditions,” in:Some Applications of Functional Analysis to Problems of Mathematical Physics, 3–17, Novosibirsk (1989).

  12. A. A. Arkhipova, “Some applications of reverse Hölder inequalities with a boundary integral,”Probl. Mat. Anal., No. 12, 13–29 (1992).

    MATH  Google Scholar 

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Translated fromProblemy Matematicheskogo Analiza, No. 15, 1995, pp. 47–69.

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Arkhipova, A.A. On the regularity of solutions of boundary-value problem for quasilinear elliptic systems with quadratic nonlinearity. J Math Sci 80, 2208–2225 (1996).

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