Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 371-394.

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We define and study Musielak-Orlicz-Sobolev spaces with zero boundary values on any metric space endowed with a Borel regular measure. We extend many classical results, including completeness, lattice properties and removable sets, to Musielak-Orlicz-Sobolev spaces on metric measure spaces. We give sufficient conditions which guarantee that a Sobolev function can be approximated by Lipschitz continuous functions vanishing outside an open set. These conditions are based on Hardy type inequalities.
DOI : 10.1007/s10587-016-0262-1
Classification : 31B15, 46E35
Mots-clés : Sobolev space; metric measure space; Hajłasz-Sobolev space; Musielak-Orlicz space; capacity; variable exponent; zero boundary values 
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     title = {Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces},
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Ohno, Takao; Shimomura, Tetsu. Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 371-394. doi : 10.1007/s10587-016-0262-1. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0262-1/

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