Skip to main content
Log in

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

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript


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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature Cited

  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).

    MATH  Google Scholar 

  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.

  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 

  4. 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 

  5. A. A. Arkhipova, “On the Regularity of the Oblique Derivative Problem for Quasilinear Elliptic Systems,” Preprint 93-132, Dept. of Math., CWRU, Cleveland.

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

  7. 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 

Download references


Additional information

Dedicated to V. A. Solonnikov on his sixtieth anniversary

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 213, 1994, pp. 5–13.

Translated by S. Yu. Pilyugin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arkhipova, A.A. On the regularity of the oblique derivative problem for quasilinear elliptic systems. J Math Sci 84, 817–822 (1997).

Download citation

  • Received:

  • Issue Date:

  • DOI: