Higher integrability for weak solutions of higher order degenerate parabolic systems

Annales Academiae Scientiarum Fennicae Mathematica

Volumn 33, Issue , 2008, Pages 387-412

  Bögelein, Verena ^a  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

Degenerate parabolic systems; Higher integrability; Higher order; Parabolic p Laplacean

Indexed keywords

EID: 59949101181     PISSN: 1239629X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. ACERBI, E., and G. MINGIONE: Gradient estimates for a class of parabolic systems. - Duke Math. J. 136, 2007, 285-320.
2. ADAMS, R. A.: Sobolev spaces. - Academic Press, New York, 1978.
3. BÖGELEIN, V.: Regularity results for weak and very weak solutions of higher order parabolic systems. - Ph.D. Thesis, 2007.
4. COIFMAN, R. R., and G. WEISS: Analyse harmonique non-commutative sur certains espaces homogenes. - Springer-Verlag, Berlin-Heidelberg-New York, 1971.
5. DIBENEDETTO, E.: Degenerate parabolic equations. - Springer-Verlag, Universitext, New York, NY, 1993.
6. DIBENEDETTO, E., and A. FRIEDMAN: Hölder estimates for non-linear degenerate parabolic systems. - J. Reine Angew. Math. 357, 1985, 1-22.
7. DUZAAR, F., A. GASTEL, and J. F. GROTOWSKI: Optimal partial regularity for nonlinear elliptic systems of higher order. - J. Math. Sci. Univ. Tokyo 8:3, 2001, 463-499.
8. ELCRAT, A., and N. G. MEYERS: Some results on regularity for solutions of non-linear elliptic systems and quasi-regular functions. - Duke Math. J. 42, 1975, 121-136.
9. EVANS, L. C., and R. F. GARIEPY: Measure theory and fine properties of functions. - CRC Press, Boca Raton, Florida, 1992.
10. p-integrability of the partial derivatives of a quasiconformal mapping. - Acta Math. 130, 1973, 265-277.
11. GIAQUINTA, M.: Multiple integrals in the calculus of variations and nonlinear elliptic systems. - Princeton University Press, Princeton, New Jersey, 1983.
12. GIAQUINTA, M., and M. STRUWE: On the partial regularity of weak solutions of nonlinear parabolic systems. - Math. Z. 179, 1982, 437-451.
13. KINNUNEN, J., and J. L. LEWIS: Higher integrability for parabolic systems of p-Laplacian type. - Duke Math. J. 102, 2000, 253-271.
14. KINNUNEN, J., and J. L. LEWIS: Very weak solutions of parabolic systems of p-Laplacian type. - Ark. Mat. 40:1, 2002, 105-132.
15. KINNUNEN, J., and Z. SHULIN: - A local estimate for nonlinear equations with discontinuous coefficients. - Comm. Partial Differential Equations 24:11-12, 1999, 2043-2068.
16. KINNUNEN, J., and Z. SHULIN: A boundary estimate for nonlinear equations with discontinuous coefficients. - Differential Integral Equations 14:4, 2001, 475-492.
17. NIRENBERG, L.: On elliptic partial differential equations. - Ann. Sc. Norm. Super. Pisa III. Ser. 123, 1960, 115-162.
18. STREDULINSKY, E. W.: Higher integrability from reverse Hölder inequalities. - Indiana Univ. Math. J. 29, 1980, 407-413.