2000 character limit reached
Sobolev space of functions valued in a monotone Banach family (2003.10657v1)
Published 24 Mar 2020 in math.FA and math.AP
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.