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arXiv · 2404.02919

Relaxation for degenerate nonlinear functionals in the onedimensional case

Valeria Chiadò Piat·Virginia De Cicco·Anderson Melchor Hernandez
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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 $1< p<+\infty$. 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.

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Valeria Chiadò Piat, Virginia De Cicco, Anderson Melchor Hernandez. 2024-03-28. Relaxation for degenerate nonlinear functionals in the onedimensional case. https://arxiv.org/abs/2404.02919

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