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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 ${\bbfR}^N$, $$W^k_p (\Omega) \hookrightarrow L_q (\Omega)$$ 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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