2022/12/21 by Andrea Braides, Braides, Andrea · 1 citation
Mathematics · Medicine · #35R11 #74A70 #9J45 #Advanced Banach Space Theory #Analysis of PDEs (math.AP) #Electrolyte and hormonal disorders #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2212.11200
openalex publication_date 2022/12/21 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28
We show that the lower-semicontinuous envelope of a non-convex double integral may not admit a representation as a double integral. By taking an integrand with value +∞ except at three points (say -1, 0 and 1) we give a simple proof and an explicit formula for the relaxation that hopefully may shed some light on this type of problems. This is a simplified version of examples by Mora-Corral and Tellini, and Kreisbeck and Zappale, who characterize the lower-semicontinuous envelope via Young measures.