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

Authors

  • Piernicola Bettiol Brest University
  • Carlo Mariconda Università di Padova

DOI:

https://doi.org/10.6092/issn.2240-2829/16156

Keywords:

Regularity, Lipschitz, minimizing sequence, approximation, radial convexity, Lavrentiev phenomenon, growth condition, state constraint

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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Published

2023-01-09

How to Cite

Bettiol, P., & Mariconda, C. (2022). The basic problem of the calculus of variations: Du Bois-Reymond equation, regularity of minimizers and of minimizing sequences. Bruno Pini Mathematical Analysis Seminar, 13(1), 26–43. https://doi.org/10.6092/issn.2240-2829/16156

Issue

Vol. 13 No. 1 (2022): Seminars 2022

Section

Articles

License

Copyright (c) 2022 Piernicola Bettiol, Carlo Mariconda

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 Unported License.