Sharp conditions for the compactness of the Sobolev embedding on Musielak–Orlicz spaces
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DOI: 10.1002/mana.201700462
Abstract: We prove the compactness of the Sobolev embedding for Musielak–Orlicz spaces by way of simple conditions on the Matuszewska index of the underlying space. We provide counterexamples to show the sharpness of our conditions. read more here.
Keywords: sharp conditions; embedding musielak; sobolev embedding; compactness sobolev ... See more keywords
A sharp higher order Sobolev embedding
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DOI: 10.1112/mtk.70012
Abstract: We obtain sharp embeddings from the Sobolev space W0k,2(−1,1)$W^{k,2}_0(-1,1)$ into the space L1(−1,1)$L^1(-1,1)$ and determine the extremal functions. This improves on a previous estimate of the sharp constants of these embeddings due to Kalyabin. read more here.
Keywords: sobolev embedding; higher order; order sobolev; sharp higher ... See more keywords