Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces Lp(.) and Wk,p(.)

Mathematische Nachrichten

Volumn 268, Issue , 2004, Pages 31-43

  Diening, Lars ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Extension operator; Generalized Lebesgue space; Generalized Sobolev space; Riesz potential; Sobolev embedding; Variable exponent

Indexed keywords

EID: 4544323976     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.200310157     Document Type: Article

References (25)

1. E. Acerbi and G. Mingione, Regularity results for a class of functionals with non-standard growth, Arch. Ration. Mech. Anal. 156, No. 2, 121-140 (2001).
2. p(.) Mathematical Inequalities and Applications, accepted (2002).
3. p(x) preprint, Mathematische Fakultät, Albert-Ludwigs-Universität Freiburg, No. 02/2002-16.01.2002, 1-6 (2002).
4. L. Diening, Theoretical and numerical results for electrorheological fluids, Ph.D. thesis, University of Freiburg, Germany (2002).
5. p(.) and problems related to fluid dynamics, J. Reine Angew. Math., accepted.
6. p(x) norms, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 455, No. 1981, 219-225 (1999).
7. D. E. Edmunds and J. Rákosník, Sobolev embeddings with variable exponent, Studia Math. 143, No. 3, 267-293 (2000).
8. D. E. Edmunds and J. Rákosník, Sobolev embeddings with variable exponent, II, Math. Nachr. 246-247, 53-67 (2002).
9. m,p(x) (Ω), J. Math. Anal. Appl. 263, No. 2, 424-446 (2001).
10. M. R. Hestenes, Extension of the range of a differentiable function, Duke Math. J. 8, 183-192 (1941).
11. k (Ω), Comment. Math. Prace Mat. 21, No. 2, 315-324 (1980).
12. k,p(x) Czechoslovak Math. J. 41 (116), No. 4, 592-618 (1991).
13. J. Malý and W. P. Zierner, Fine regularity of solutions of elliptic partial differential equations, Amer. Math. Soc. (Providence, RI, 1997).
14. P. Marcellini, Regularity and existence of solutions of elliptic equations with p, q-growth conditions, J. Differential Equations 90, No. 1, 1-30 (1991).
15. E. J. McShane, Extension of range of functions., Bull. Am. Math. Soc. 40, 837-842 (1934).
16. J. Musielak and W. Orlicz, On modular spaces, Studia Math. 18, 49-65 (1959).
17. J. Musielak, Orlicz Spaces and Modular Spaces (Springer-Verlag, Berlin, 1983).
18. H. Nakano, Modulared Semi-Ordered Linear Spaces (Maruzen Co. Ltd., Tokyo, 1950).
19. n), Mathematical Inequalities and Applications, accepted (2002).
20. p(x) on which the Hardy-Littlewood maximal operator is not bounded, Expo. Math. 19, No. 4, 369-371 (2001).
21. M. Růžička, Electrorheological Fluids: Modeling and Mathematical Theory (Springer-Verlag, Berlin, 2000).
22. n), Dokl. Akad. Nauk 369, No. 4, 451-454 (1999).
23. n), Integral Transform. Spec. Funct. 7, No. 3-4, 261-284 (1998).
24. V. V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory, Izv. Akad. Nauk SSSR Ser. Mat. 50, No. 4, 675-710, 877 (1986).
25. V. V. Zhikov, Meyer-type estimates for solving the nonlinear Stokes system, Differ. Uravn. 33, No. 1, 107-114, 143 (1997).