Lq-differentials for weighted Sobolev spaces

Michigan Mathematical Journal

Volumn 47, Issue 1, 2000, Pages 151-161

  Björn, Jana ^a  

^a LINKÖPING UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17344385069     PISSN: 00262285     EISSN: None     Source Type: Journal    
DOI: 10.1307/mmj/1030374674     Document Type: Article

References (15)

1. J. Björn, Boundedness and differentiability a.e. for systems of elliptic equations and variationai inequalities, preprint, 1999.
2. _, Poincaré inequalities for powers and products of admissible weights, Ann. Acad. Sci. Fenn. Ser. A I Math, (to appear).
3. A. P. Calderón and A. Zygmund, Local properties of solutions of elliptic partial differential equations, Studia Math. 20 (1961), 171-225.
4. J. Cheeger, Differentiability of Lipschitz functions on metric spaces, Geom. Funct. Anal. 9 (1999), 428-517.
5. B. Franchi, P. Hajłasz, and P. Koskela, Definitions of Sobolev classes on metric spaces, Ann. Inst. Fourier (Grenoble) (to appear).
6. P. Hajłasz, Sobolev spaces on an arbitrary metric space, Potential Anal. 5 (1996), 403-415.
7. P. Hajłasz and P. Koskela, Sobolev met Poincaré, Mem. Amer. Math. Soc. (to appear).
8. P. Hajłasz and P. Strzelecki, On the differentiability of solutions of quasilinear elliptic equations, Colloq. Math. 64 (1993), 287-291.
9. J. Heinonen, T. Kilpeläinen, and O. Martio, Nonlinear potential theory of degenerate elliptic equations, Oxford Univ. Press, Oxford, 1993.
10. J. Heinonen and P. Koskela, A note on Lipschitz functions, upper gradients, and the Poincaré inequality, New Zealand J. Math. 28 (1999), 37-42.
11. J. Ježková, Boundedness and pointwise differentiability of weak solutions to quasi-linear elliptic differential equations and variational inequalities, Comment. Math. Univ. Carolin. 35 (1994), 63-80.
12. G. Karch and T. Ricciardi, Note on Lorentz spaces and differentiability of weak solutions to elliptic equations, Bull. Polish Acad. Sci. Math. 45 (1997), 111-116.
13. N. Shanmugalingam, Newtonian spaces: An extension of Sobolev spaces to metric measure spaces, Rev. Mat. Iberoamericana (to appear).
14. E. M. Stein, Singular integrals and differentiability of functions, Princeton Univ. Press, Princeton, NJ, 1970.
15. W. P. Ziemer, Weakly differentiate functions, Springer-Verlag, New York, 1989.