Relaxation for degenerate nonlinear functionals in the onedimensional case

2024/03/28 by Valeria Chiadò Piat, Virginia De Cicco, Piat, Valeria Chiadò +3 · 1 citation
Mathematics · #26A15 #49J45 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2404.02919

openalex publication_date 2024/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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 Poincaré inequality involving an auxiliary weight.

Cited by

• Minimization of Degenerate Nonlinear Functionals under Radial Symmetry

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