Preprint

Inserted: 27 mar 2024
Last Updated: 29 aug 2024

Year: 2024

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 (De Cicco, Serra Cassano), 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.

Keywords: relaxation, degenerate variational integrals, Lower Semicontinuity, Poincaré inequalities, weight

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