Uniqueness and maximal regularity for nonlinear elliptic systems of n-Laplace type with measure valued right hand side

Journal fur die Reine und Angewandte Mathematik

Volumn 2000, Issue 520, 2000, Pages 1-35

  Dolzmann, Georg ^a,b   Hungerbühler, Norbert ^a,b   Müller, Stefan ^a,b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040194290     PISSN: 00754102     EISSN: 14355345     Source Type: Journal    
DOI: 10.1515/crll.2000.022     Document Type: Article

References (30)

1. E. Acerbi, N. Fusco, An approximation lemma for W1, p-functions in: Proceedings of the symposion on material instabilities and continuum mechanics, Oxford Science Publications (1988), 1-5.
2. P. Bénilan, L. Boccardo, T. Gallouët, R. Gariepy, M. Pierre, J. L. Vazquez, An L*-theory of existence and uniqueness of solutions of nonlinear elliptic equations Ann. Sc. Norm. Sup. Pisa Cl. Sci. (4) 22 (1995), 241-273.
3. L. Boccardo, T. Gallouët, Non-linear elliptic and parabolic equations involving measure data J. Funct. Anal. 87 (1989), 149-169.
4. L. Boccardo, T. Gallouët, L. Orsina, Existence and uniqueness of entropy solutions for nonlinear elliptic eqations with measure data Ann. Inst. H. Poincaré Anal. Non Lin. 13 (1996), no. 5, 539-551.
5. L. Boccardo, F. Murat, Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations Nonlin. Anal. 19 (1992), 581-597.
6. P. L. Butzer, H. Berens, Semi-groups of operators and approximation Springer, 1967.
7. G. Dal Maso, F. Murat, Almost everywhere convergence of gradients of solutions to nonlinear elliptic systems Nonlin. Anal. 31 (1998), 405-412.
8. G. Dal Maso, F. Murat, L. Orsina, A. Prignet, Definition and existence of renormalized solutions of elliptic equations with general measure data C. R. Acad. Sci. Paris Sér. 1 Math. 235 (1997), 481-486.
9. E. DiBenedetto, J. Manfredi, On the higher integrability of the gradient of weak solutions of certain degenerate elliptic systems Amer. J. Math. 115 (1993), 1107-1134.
10. G. Dolzmann, N. Hungerbëhler, S. Müller, Non-linear elliptic systems with measure-valued right hand side Math. Z. 226 (1997), no. 4, 545-574.
11. L. C. Evans, R. Gariepy, Measure theory and fine properties of functions CRC Press, Boca Raton 1992.
12. V. Ferone, N. Fusco, VMO solutions of the N-Laplacian with measure data C. R. Acad. Sci. Paris Sér. 1 Math. 325 (1997), no. 4, 365-370.
13. M. Fuchs, J. Reuling, Non-linear elliptic systems involving measure data Rend. Mat. 15 (1995), 311-319.
14. M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems Princeton University Press, 1983.
15. I. S. Gradshteyn and I. M. Ryzhik, Table of integrals series, and products, Academic Press, Boston 1994.
16. L. Greco, T. Iwaniec, C. Sbordone, Inverting the p harmonic operator Manuscr. Math. 92 (1997), no. 2, 249-258.
17. R. A. Hunt, On L(p q) spaces, Enseign. Math. (II) 12 (1966), 249-276.
18. F. John, L. Nirenberg, On functions of bounded mean oscillation Comm. Pure Appl. Math. 14 (1961), 415-426.
19. T. Kilpeläinen, X. Xu, On the uniqueness problem for quasilinear elliptic equations involving measures Rev. Mat. Iberoamer. 12 (1996), no. 2, 461-475.
20. R. Landes, On the existence of weak solutions of perturbed systems with critical growth J. reine angew. Math. 393 (1989), 21-38.
21. J. L. Lewis, On very weak solutions of certain elliptic systems Comm. Part. Diff. Equ. 18 (1993), 1515-1537.
22. F. C. Liu, A Luzin type property of Sobolev functions Indiana Univ. Math. J. 26 (1977), no. 4, 645-651.
23. J. H. Michael, W. P. Ziemer, A Lusin type approximation of Sobolev functions by smooth functions Classical real analysis (Madison, Wis. 1982)
24. Contemp. Math. 42 (1985), 135-167.
25. C. B. Morrey, Multiple integrals in the calculus of variations Grundl. math. Wiss. 130, Springer-Verlag, New York 1966.
26. F. Murat, Soluciones renormalizadas de EDP elipticas no lineales Publ. Labor. Anal. Num. R93023 (1993).
27. L. Simon, Theorems on regularity and singularity of energy minimizing maps Lect. math. ETH Zürich, Birkhäuser, Basel 1996.
28. L. Simon, Schauder estimates by scaling Calc. Var. 5 (1997), 391-407.
29. E. Stein, Singular integrals and differentiability properties of functions Princeton University Press, Princeton 1970.
30. G. Talenti, Nonlinear elliptic equations rearrangements of functions and Orlicz spaces, Ann. Mat. Pura Appl. (4) 120 (1979), 159-184.