English

Relaxation for degenerate nonlinear functionals in the onedimensional case

Analysis of PDEs 2025-01-28 v2

Abstract

In this study, we approach the analysis of a degenerate nonlinear functional in one dimension, accommodating a degenerate weight ww. Our investigation focuses on establishing an explicit relaxation formula for a functional exhibiting pp-growth for 1<p<+1< p<+\infty. We adopt the approach developed in [6], where some assumptions like doubling or Muckenhoupt conditions are dropped. Our main tools consist of proving the validity of a weighted Poincar\'e inequality involving an auxiliary weight.

Keywords

Cite

@article{arxiv.2404.02919,
  title  = {Relaxation for degenerate nonlinear functionals in the onedimensional case},
  author = {Valeria Chiadò Piat and Virginia De Cicco and Anderson Melchor Hernandez},
  journal= {arXiv preprint arXiv:2404.02919},
  year   = {2025}
}
R2 v1 2026-06-28T15:43:18.519Z