Calculus of Variations and Geometric Measure Theory

N. Evseev - A. Menovschikov

Sobolev space of functions valued in a monotone Banach family

created by evseev on 25 Mar 2020



Inserted: 25 mar 2020

Year: 2020

ArXiv: 2003.10657 PDF


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.