Some theorems about the validity of the Euler-Lagrange equation are proved. In particular, Lagrangians without regularity hypothesis or without growth assumptions are considered. Moreover, a result about the non-occurrence of the Lavrentiev phenomenon in the scalar case is proved.
(2012). Progresses on some classical problems of the calculus of variations. (Tesi di dottorato, Università degli Studi di Milano-Bicocca, 2012).
Progresses on some classical problems of the calculus of variations
BONFANTI, GIOVANNI
2012
Abstract
Some theorems about the validity of the Euler-Lagrange equation are proved. In particular, Lagrangians without regularity hypothesis or without growth assumptions are considered. Moreover, a result about the non-occurrence of the Lavrentiev phenomenon in the scalar case is proved.
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