Relaxation for a degenerate functional with linear growth in the onedimensional case

Abstract

In this work, we study the relaxation of a degenerate functional with linear growth, depending on a weight $w$ that does not exhibit doubling or Muckenhoupt-type conditions. In order to obtain an explicit representation of the relaxed functional and its domain, our main tools for are Sobolev inequalities with double weight.

arXiv commentarXiv admin note: substantial text overlap with arXiv:2404.02919