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 . Our investigation focuses on establishing an explicit relaxation formula for a functional exhibiting -growth for . 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}
}