Sobolev embeddings with variable exponent
Studia Mathematica, Tome 143 (2000) no. 3, pp. 267-293
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let Ω be a bounded open subset of $ℝ^{n}$ with Lipschitz boundary and let $p:\overline{Ω} → [1,∞)$ be Lipschitz-continuous. We consider the generalised Lebesgue space $L^{p(x)}(Ω)$ and the corresponding Sobolev space $W^{1,p(x)}(Ω)$, consisting of all $f ∈ L^{p(x)}(Ω)$ with first-order distributional derivatives in $L^{p(x)}(Ω)$. It is shown that if 1 ≤ p(x) n for all x ∈ Ω, then there is a constant c > 0 such that for all $f∈ W^{1,p(x)}(Ω)$, $|f|_{M,Ω} ≤ c|f|_{1,p,Ω}$. Here $|·|_{M,Ω}$ is the norm on an appropriate space of Orlicz-Musielak type and $|·|_{1,p,Ω}$ is the norm on $W^{1, p(x)}(Ω)$. The inequality reduces to the usual Sobolev inequality if $sup_Ω p
@article{10_4064_sm_143_3_267_293,
author = {David Edmunds and Ji\v{r}{\'\i} R\'akosn{\'\i}k},
title = {Sobolev embeddings with variable exponent},
journal = {Studia Mathematica},
pages = {267--293},
publisher = {mathdoc},
volume = {143},
number = {3},
year = {2000},
doi = {10.4064/sm-143-3-267-293},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-143-3-267-293/}
}
TY - JOUR AU - David Edmunds AU - Jiří Rákosník TI - Sobolev embeddings with variable exponent JO - Studia Mathematica PY - 2000 SP - 267 EP - 293 VL - 143 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-143-3-267-293/ DO - 10.4064/sm-143-3-267-293 LA - en ID - 10_4064_sm_143_3_267_293 ER -
David Edmunds; Jiří Rákosník. Sobolev embeddings with variable exponent. Studia Mathematica, Tome 143 (2000) no. 3, pp. 267-293. doi: 10.4064/sm-143-3-267-293
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