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Sobolev embedding theorems for spaces $$W^{k,p(x)}(\Omega)$$. (English) Zbl 0995.46023
The well-known Sobolev embedding theorem in $${\mathbb{R}}^N$$, $W^k_p (\Omega) \hookrightarrow L_q (\Omega)$ is extended to cases with variable integrability: $W^k_{p(x)} (\Omega) \hookrightarrow L_{q(x)} (\Omega).$ This applies also to compactness assertions if the domain $$\Omega$$ is bounded.

##### MSC:
 4.6e+36 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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##### References:
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