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math.FA2020
Vector-valued Sobolev spaces based on Banach function spaces
Nikita Evseev
It is known that for Banach valued functions there are several approaches to define a Sobolev class. We compare the usual definition via weak derivatives with the Reshetnyak-Sobole…
math.FA2020★ 5 cited
Sobolev space of functions valued in a monotone Banach family
Nikita Evseev, Alexander Menovschikov
We apply the metrical approach to Sobolev spaces, which arise in various evolution PDEs. Functions from those spaces are defined on an interval and take values in a family of Banac…