Abstract
In this paper we prove that if a functional has bounded minimum u, then is is possible, using Ekeland’s \(\varepsilon\)-variational principle, to build a minimizing sequence which is uniformly convergent to u.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Boccardo, L., Ferone, V., Fusco, N., Orsina, L.: Regularity of minimizing sequences for functionals of the calculus of variations via the Ekeland principle. Differ. Integr. Equ. 12(1), 119–135 (1999)
Boccardo, L., Giachetti, D.: A nonlinear interpolation result with application to the summability of minima of some integral functionals. Discrete Continuous Dyn. Syst. Ser. B 11(1), 31–42 (2009)
de Figueiredo, D.G.: Lectures on the Ekeland variational principle with applications and detours. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 81. Published for the Tata Institute of Fundamental Research, Bombay; by Springer, Berlin (1989)
Ekeland, I.: On the variational principle. J. Math. Anal. Appl. 47, 324–353 (1974)
Ekeland, I.: Nonconvex minimization problems. Bull. Am. Math. Soc. (N.S.) 1(3), 443–474 (1979)
Ekeland, I., Temam, R.: Analyse convexe et problèmes variationnels. Collection Études Mathématiques. Dunod; Gauthier-Villars, Paris-Brussels-Montreal, Que. (1974)
Ladyženskaja, O.A., Uralceva, N.N.: Équations aux dérivées partielles de type elliptique. Traduit par G. Roos. Monographies Universitaires de Mathématiques, vol. 31. Dunod, Paris (1968)
Leray, J., Lions, J.-L.: Quelques résulatats de Višik sur les problèmes elliptiques nonlinéaires par les méthodes de Minty-Browder. Bull. Soc. Math. Fr. 93, 97–107 (1965)
Stampacchia, G.: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier (Grenoble) 15(fasc. 1), 189–258 (1965)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Additional information
Dedicated to Djairo for his 40th birthday, twice
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Boccardo, L., Orsina, L. (2015). A consequence of Djairo’s Lectures on the Ekeland variational principle. In: Nolasco de Carvalho, A., Ruf, B., Moreira dos Santos, E., Gossez, JP., Monari Soares, S., Cazenave, T. (eds) Contributions to Nonlinear Elliptic Equations and Systems. Progress in Nonlinear Differential Equations and Their Applications, vol 86. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-19902-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-19902-3_3
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-19901-6
Online ISBN: 978-3-319-19902-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)