Issue:

SSRSMI, Number 1, Volume XXIX

Section:

Volume 29, Number 1

Abstract:

We generalize a coincidence result from the case of Sobolev-type spaces to the case of Orlicz-Sobolev spaces corresponding to a doubling Young function, in the setting of doubling metric measure spaces. We consider three types of Orlicz-Sobolev spaces: (i) a space of Newtonian type; (ii) a space associated to a generalized Poincaré inequality; (iii) a space defined as the closure of the class of Orlicz functions that are locally Lipschitz, under some norm involving an abstract differential operator.

Keywords:

metric measure space, weak upper gradient, Orlicz-Sobolev space, locally Lipschitz func-tions, Orlicz-Poincaré inequality.

Code [ID]:

SSRSMI201901V29S01A0010 [0005077]

Note:

DOI:

Full paper:

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