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On embeddings and traces in Sobolev spaces with weights of power type

100%

Rákosník J.

Banach Center Publications

1989

tom 22

nr 1

331-339

Sobolev embeddings with variable exponent

84%

Edmunds D. E., Rákosník J.

Studia Mathematica

2000

tom 143

nr 3

267-293

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

Ograniczanie wyników

1 Banach Center Publications

1 Studia Mathematica

2 Rákosník J.

1 Edmunds D. E.

1 2000

1 1989

Wyniki wyszukiwania

On embeddings and traces in Sobolev spaces with weights of power type

Sobolev embeddings with variable exponent