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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.

46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Full Text: DOI
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