Calculus of Variations and Geometric Measure Theory

A. Ponce - D. Spector

A decomposition by non-negative functions in the Sobolev space $W^{k, 1}$

created by spector on 13 Jul 2018



Inserted: 13 jul 2018
Last Updated: 13 jul 2018

Year: 2018


We show how a strong capacitary inequality can be used to give a decomposition of any function in the Sobolev space $W^{k,1}(\mathbb{R}^d)$ as the difference of two non-negative functions in the same space with control of their norms.