The Lavrentiev phenomenon is surveyed firstly for the one-dimensional Lagrange problem of the calculus of variations, starting from the classical examples and results. The approach based on the relaxation point of view is especially emphasized and examples are presented where the Lavrentiev gap is explicitly computed. The case of integrands depending on higher-order derivatives is also discussed with examples. Cases in which the Lavrentiev phenomenon can be excluded are listed (with a sketch of the proofs). Finally the multiple integral case is considered, with examples exhibiting the phenomenon. Some open problems are also mentioned.
A survey on old and recent results about the gap phenomenon in the calculus of variations / Belloni, Marino; Buttazzo, G.. - 331:(1995), pp. 1-27. (Intervento presentato al convegno Recent developments in well-posed variational problems nel 1994).
A survey on old and recent results about the gap phenomenon in the calculus of variations
BELLONI, Marino;
1995-01-01
Abstract
The Lavrentiev phenomenon is surveyed firstly for the one-dimensional Lagrange problem of the calculus of variations, starting from the classical examples and results. The approach based on the relaxation point of view is especially emphasized and examples are presented where the Lavrentiev gap is explicitly computed. The case of integrands depending on higher-order derivatives is also discussed with examples. Cases in which the Lavrentiev phenomenon can be excluded are listed (with a sketch of the proofs). Finally the multiple integral case is considered, with examples exhibiting the phenomenon. Some open problems are also mentioned.| File | Dimensione | Formato | |
|---|---|---|---|
|
1996-BeBu-Genova.pdf
non disponibili
Tipologia:
Documento in Post-print
Licenza:
Creative commons
Dimensione
191.02 kB
Formato
Adobe PDF
|
191.02 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
