Skip to main content
Log in

Very weak solutions of parabolic systems ofp-Laplacian type

  • Published:
Arkiv för Matematik

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.

References

  1. Acerbi, E. andFusco, N., Semicontinuity problems in the calculus of variations,Arch. Rational. Mech. Anal. 86 (1984), 125–145.

    Article  MathSciNet  Google Scholar 

  2. DiBenedetto, E.,Degenerate Parabolic Equations, Springer-Verlag, Berlin-Heidelberg-New York, 1993.

    Google Scholar 

  3. Iwaniec, T.,p-harmonic tensors and quasiregular mappings,Ann. of Math. 136 (1992), 589–624.

    MATH  MathSciNet  Google Scholar 

  4. Iwaniec, T. andSbordone, C., Weak minima of variational integrals,J. Reine Angew. Math. 454 (1994), 143–161.

    MathSciNet  Google Scholar 

  5. Kilpeläinen, T. andLindqvist, P., On the Dirichlet boundary value problem for a degenerate parabolic equation,Siam J. Math. Anal. 27 (1996), 661–683.

    Article  MathSciNet  Google Scholar 

  6. Kinnunen, J. andLewis, J. L., Higher integrability for parabolic systems ofp-Laplacian type,Duke Math. J. 102 (2000), 253–271.

    Article  MathSciNet  Google Scholar 

  7. Lewis, J. L., On very weak solutions to certain elliptic systems,Comm. Partial Differential Equations 18 (1993), 1515–1537.

    MATH  MathSciNet  Google Scholar 

  8. Meyers, N. G., AnL p-estimate for the gradient of solutions of second order elliptic divergence equations,Ann. Scuola Norm. Sup. Pisa Cl. Sci. 17 (1963), 189–206.

    MATH  MathSciNet  Google Scholar 

  9. Meyers, N. G. andElcrat, A., Some results on regularity for solutions of nonlinear elliptic systems and quasi-regular functions,Duke Math. J. 42 (1975), 121–136.

    MathSciNet  Google Scholar 

  10. Stein, E. M.,Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N. J., 1970.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research was partially conceived at the Mittag-Leffler Institute during a special year in PDE's in 1999–2000. The authors wish to thank the Institute for gracious hospitality. The first author was also supported by the Academy of Finland and the second author by an NSF Grant.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kinnunen, J., Lewis, J.L. Very weak solutions of parabolic systems ofp-Laplacian type. Ark. Mat. 40, 105–132 (2002). https://doi.org/10.1007/BF02384505

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02384505

Keywords

Navigation