Relaxation for degenerate nonlinear functionals in the onedimensional case
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<+∞. 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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