Archivio Istituzionale della RicercaIn this study, we approach the analysis of a degenerate nonlinear functional in one dimension, accommodating a degenerate weight w. Our investigation focuses on establishing an explicit relaxation formula for a functional exhibiting p-growth for finite p>1. We adopt the approach developed in [https://cvgmt.sns.it/paper/6038/] where some assumptions like doubling or Muckenhoupt conditions are dropped. Our main tools consist of proving the validity of a weighted Poincaré inequality involving an auxiliary weight.
Relaxation for degenerate nonlinear functionals in the onedimensional case / Chiado' Piat, V.; De Cicco, V.; Melchor Hernandez, A.. - In: NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1420-9004. - ELETTRONICO. - 32:4(2025), pp. 1-19. [10.1007/s00030-025-01058-2]
Relaxation for degenerate nonlinear functionals in the onedimensional case
V. Chiado' Piat;
2025
Abstract
In this study, we approach the analysis of a degenerate nonlinear functional in one dimension, accommodating a degenerate weight w. Our investigation focuses on establishing an explicit relaxation formula for a functional exhibiting p-growth for finite p>1. We adopt the approach developed in [https://cvgmt.sns.it/paper/6038/] where some assumptions like doubling or Muckenhoupt conditions are dropped. Our main tools consist of proving the validity of a weighted Poincaré inequality involving an auxiliary weight.
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https://hdl.handle.net/11583/2999524