Sobolev embeddings with variable exponent
Studia Mathematica (2000)
- Volume: 143, Issue: 3, page 267-293
- ISSN: 0039-3223
Access Full Article
topAbstract
topHow to cite
topEdmunds, David, and Rákosník, Jiří. "Sobolev embeddings with variable exponent." Studia Mathematica 143.3 (2000): 267-293. <http://eudml.org/doc/216819>.
@article{Edmunds2000,
abstract = {},
author = {Edmunds, David, Rákosník, Jiří},
journal = {Studia Mathematica},
keywords = {generalised Lebesgue spaces; embeddings; extension operators; Sobolev space; space of Orlicz-Musielak type; Sobolev inequality},
language = {eng},
number = {3},
pages = {267-293},
title = {Sobolev embeddings with variable exponent},
url = {http://eudml.org/doc/216819},
volume = {143},
year = {2000},
}
TY - JOUR
AU - Edmunds, David
AU - Rákosník, Jiří
TI - Sobolev embeddings with variable exponent
JO - Studia Mathematica
PY - 2000
VL - 143
IS - 3
SP - 267
EP - 293
AB -
LA - eng
KW - generalised Lebesgue spaces; embeddings; extension operators; Sobolev space; space of Orlicz-Musielak type; Sobolev inequality
UR - http://eudml.org/doc/216819
ER -
References
top- [BMS] L. Boccardo, P. Marcellini and C. Sbordone, -regularity for variational problems with sharp nonstandard growth conditions, Boll. Un. Mat. Ital. A (7) 4 (1990), 219-225. Zbl0711.49058
- [DL] J. Deny et J.-L. Lions, Les espaces du type de Beppo Levi, Ann. Inst. Fourier (Grenoble) 5 (1953/54), 305-370. Zbl0065.09903
- [ER] D. E. Edmunds and J. Rákosník, Density of smooth functions in , Proc. Roy. Soc. London Ser. A 437 (1992), 229-236. Zbl0779.46027
- [EvR] W. D. Evans and J. Rákosník, Anisotropic Sobolev spaces and a quasidistance function, Bull. London Math. Soc. 23 (1991), 59-66. Zbl0736.46020
- [FS] N. Fusco and C. Sbordone, Some remarks on the regularity of minima of anisotropic integrals, Comm. Partial Differential Equations 18 (1993), 153-167. Zbl0795.49025
- [G] M. Giaquinta, Growth conditions and regularity, a counterexample, Manuscripta Math. 59 (1987), 245-248. Zbl0638.49005
- [Gu] M. de Guzmán, A covering lemma with application to differentiability of measures and singular integral operators, Studia Math. 34 (1970), 299-317. Zbl0192.48804
- [H] M. Hestenes, Extension of the range of a differentiable function, Duke Math. J. 8 (1941), 183-192. Zbl0024.38602
- [Hu] H. Hudzik, The problems of separability, duality, reflexivity and of comparison for generalized Orlicz-Sobolev space , Comment. Math. Prace Mat. 21 (1980), 315-324.
- [KR] O. Kováčik and J. Rákosník, On spaces and , Czechoslovak Math. J. 41 (116) (1991), 592-618.
- [KJF] A. Kufner, O. John and S. Fučík, Function Spaces, Noordhoff, Leyden, and Academia, Praha, 1977.
- [LU] O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Equations, Academic Press, New York, 1968.
- [M1] P. Marcellini, Regularity of minimizers of integrals of the calculus of variations with non-standard growth conditions, Arch. Rational Mech. Anal. 105 (1989), 267-284. Zbl0667.49032
- [M2] P. Marcellini, Regularity for elliptic equations with general growth conditions, J. Differential Equations 105 (1993), 296-333. Zbl0812.35042
- [Ma] P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge Univ. Press, Cambridge, 1999. Zbl0911.28005
- [McS] E. J. McShane, Extension of range of functions, Bull. Amer. Math. Soc. 40 (1934), 837-842. Zbl0010.34606
- [MS] N. G. Meyers and J. Serrin, H=W, Proc. Nat. Acad. Sci. U.S.A. 51 (1964), 1055-1056.
- [Mu] J. Musielak, Orlicz Spaces and Modular Spaces, Springer, Berlin, 1983.
- [R1] M. Růžička, Electrorheological fluids: mathematical modelling and existence theory, Habilitationsschrift, Universität Bonn, 1998.
- [R2] M. Růžička, Flow of shear dependent electrorheological fluids, C. R. Acad. Sci. Paris Sér. I 329 (1999), 393-398. Zbl0954.76097
- [Ta] G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura Appl. 110 (1976), 353-372. Zbl0353.46018
- [Zh] V. V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory, Math. USSR-Izv. 29 (1987), 33-66. Zbl0599.49031
- [Z] W. P. Ziemer, Weakly Differentiable Functions, Grad. Texts in Math. 120, Springer, New York, 1989.
Citations in EuDML Documents
top- Mohamed Laghzal, Abdelouahed El Khalil, Abdelfattah Touzani, A Weighted Eigenvalue Problems Driven by both -Harmonic and -Biharmonic Operators
- Makkia Dammak, Abir Amor Ben Ali, Said Taarabti, Positive solutions for concave-convex elliptic problems involving -Laplacian
- Jens Habermann, Full Regularity for Convex Integral Functionals with Growth in Low Dimensions
- Mihai Mihăilescu, Vicenţiu Rădulescu, Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces
- Mihai Mihăilescu, On a class of nonlinear problems involving a -Laplace type operator
- Michela Eleuteri, Hölder continuity results for a class of functionals with non-standard growth
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.