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arXiv · 2003.10657

Sobolev space of functions valued in a monotone Banach family

Nikita Evseev·Alexander Menovschikov
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Abstract

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 Banach spaces. In this case we adapt the definition of Newtonian spaces. For a monotone family, we show the existence of weak derivative, obtain an isomorphism to the standard Sobolev space, and provide some scalar characteristics.

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Nikita Evseev, Alexander Menovschikov. 2020-03-24. Sobolev space of functions valued in a monotone Banach family. https://doi.org/10.1016/j.jmaa.2020.124440

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