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Journal Articles Bruno Pini Mathematical Analysis Seminar (BPMAS) Year : 2023

The basic problem of the calculus of variations: Du Bois-Reymond equation, regularity of minimizers and of minimizing sequences

Il problema classico del calcolo delle variazioni: l'equazione di Du Bois-Reymond, la regolarità dei minimi e delle successioni minimizzanti

Abstract

We consider the basic problem of the Calculus of variations of minimizing an integral functional among the absolutely continuous functions that satisfy prescribed boundary conditions. We resume the state of the art and our recent contributions concerning the validity of the Du Bois-Reymond condition, and the Lipschitz regularity of the minimizers and of minimizing sequences (e.g., Lavrentiev phenomenon).
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Dates and versions

hal-04315765 , version 1 (30-11-2023)

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Piernicola Bettiol, Carlo Mariconda. The basic problem of the calculus of variations: Du Bois-Reymond equation, regularity of minimizers and of minimizing sequences. Bruno Pini Mathematical Analysis Seminar (BPMAS) , 2023, ⟨10.6092/issn.2240-2829/16156⟩. ⟨hal-04315765⟩
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