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 , and ) 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.
A simplified counterexample to the integral representation of the relaxation of double integrals / Braides, A.. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - 362:(2024), pp. 487-491. [10.5802/crmath.558]
A simplified counterexample to the integral representation of the relaxation of double integrals
Braides A.
2024-01-01
Abstract
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 , and ) 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.| File | Dimensione | Formato | |
|---|---|---|---|
|
CRMATH_2024__362_G5_487_0.pdf
accesso aperto
Tipologia:
Versione Editoriale (PDF)
Licenza:
Creative commons
Dimensione
350.69 kB
Formato
Adobe PDF
|
350.69 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
