Vector-valued Sobolev spaces based on Banach function spaces
نویسندگان
چکیده
It is known that there are several approaches to define a Sobolev class for Banach valued functions. We compare the usual definition via weak derivatives with Reshetnyak–Sobolev space and Newtonian space; in particular, we provide sufficient conditions when all three agree. Also, revise difference quotient criterion property of Lipschitz mapping preserve it acting as superposition operator.
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ژورنال
عنوان ژورنال: Nonlinear Analysis-theory Methods & Applications
سال: 2021
ISSN: ['1873-5215', '0362-546X']
DOI: https://doi.org/10.1016/j.na.2021.112479