Journal of Mathematical Sciences

, Volume 84, Issue 1, pp 817–822 | Cite as

On the regularity of the oblique derivative problem for quasilinear elliptic systems

  • A. A. Arkhipova


This note continues the author's investigations of the regularity problem for quasilinear elliptic systems with nonlinear boundary conditions. Partial regularity of weak solutions of the oblique derivative problem is proved here. Bibliography: 7 titles.


Boundary Condition Weak Solution Elliptic System Nonlinear Boundary Partial Regularity 
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Literature Cited

  1. 1.
    A. A. Arkhipova, “Partial regularity of solutions of quasilinear elliptic systems with a non-smooth condition on the conormal derivative,”Mat. Sb.,184, 87–104 (1993).MATHGoogle Scholar
  2. 2.
    A. A. Arkhipova, “Inverse Hölder inequalities with boundary integral andL p-estimates in the problems with Neumann condition,” in:Some Applications of Functional Analysis to Problems of Mathematical Physics [in Russian], Novosibirsk (1990), pp. 3–20.Google Scholar
  3. 3.
    A. A. Arkhipova, “Some applications of inverse Hölder inequalities with boundary integral,” in:Problems of Mathematical Analysis, LGU, Leningrad,12 (1992) pp. 5–19.Google Scholar
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    A. A. Arkhipova, “L p-estimates of gradients for initial boundary-value problems for quasilinear parabolic systems,” in:Problems of Mathematical Analysis, LGU, Leningrad,13 (1992), pp. 4–21.Google Scholar
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    A. A. Arkhipova, “On the Regularity of the Oblique Derivative Problem for Quasilinear Elliptic Systems,” Preprint 93-132, Dept. of Math., CWRU, Cleveland.Google Scholar
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    M. Giaquinta,Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Princeton U. Press (1983).Google Scholar
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    M. Giaquinta and G. Modica, “Nonlinear systems of the type of the stationary Navier-Stokes systems,”J. Reine Angew. Math.,330, 173–214 (1982).MathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • A. A. Arkhipova

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