Some problems in the Calculus of Variations

Arrigo Cellina

Published: 2017-06-30

Vol. 31 (2017)

Some problems in the Calculus of Variations

Arrigo Cellina

Abstract

We present some results and open problems in the Calculus of Variations.

Keywords:

regularity of solutions , Lagrangians , Euler–Lagrange equation

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Cellina, A. (2017). Some problems in the Calculus of Variations. Annales Mathematicae Silesianae, 31, 5–55. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13937

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References

1. Brézis H., Multiplicateur de Lagrange en Torsion Elastoplastique, Arch. Rat. Mech. Anal. 49 (1972), 32–40.
2. Cellina A., The classical problem of the calculus of variations in the autonomous case: relaxation and Lipschitzianity of solutions, Trans. Amer. Math. Soc. 356 (2004), 415–426.
3. Cellina A., Strict convexity and the regularity of solutions to variational problems, ESAIM Control Optim. Calc. Var. 22 (2016), 862–871.
4. Cellina A., The regularity of solutions to the p-Laplace equation for 1<p<2, ESAIM Control Optim. Calc. Var. To appear.
5. Cellina A., The validity of the Euler–Lagrange equation for solutions to variational problems, J. Fixed Point Theory Appl. 15 (2014), 577–586.
6. Cellina A., A case of regularity of solutions to nonregular problems, SIAM J. Control Optim. 53 (2015), 2835–2845.
7. Cellina A., Ferriero A., Existence of Lipschitzian solutions to the classical problem of the calculus of variations in the autonomous case, Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003), 911–919.
8. Cellina A., Perrotta S., On minima of radially symmetric functionals of the gradient, Nonlinear Anal. 23 (1994), no. 2, 239–249.
9. Cellina A., Staicu V., The existence of solutions to variational problems of slow growth, J. Differential Equations 260 (2016), 5834–5846.
10. Cellina A., Treu G., Zagatti S., On the minimum problem for a class of non-coercive functionals, J. Differential Equations 127 (1996), 225–262.
11. Dacorogna B., Direct methods in the Calculus of Variations, Second edition, Springer, Berlin, 2008.
12. Degiovanni M., Marzocchi M., On the Euler–Lagrange equation for functionals of the calculus of variations without upper growth conditions, SIAM J. Control Optim. 48 (2009), 2857–2870.
13. Esposito L., Leonetti F., Mingione G., Regularity results for minimizers of irregular integrals with (p, q) growth, Forum Math. 14 (2002), 245–272.
14. Jenkins H., Serrin J., The Dirichlet problem for the minimal surface equation in higher dimensions, J. Reine Angew. Math. 229 (1968), 170–187.
15. Rockafellar R.T., Convex Analysis, Princeton University Press, Princeton, 1972. Google Scholar

Vol. 31 (2017)
Published: 2017-09-13

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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