Bellazzini, Jacopo and Siciliano, Gaetano (2011) Scaling properties of functionals and existence of constrained minimizers. Journal of Functional Analysis, Vol. 261 (9), p. 2486-2507. ISSN 0022-1236. eISSN 1096-0783. Article.
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In this paper we develop a new method to prove the existence of minimizers for a class of constrained
minimization problems on Hilbert spaces that are invariant under translations. Our method permits to exclude
the dichotomy of the minimizing sequences for a large class of functionals. We introduce family of maps, called scaling paths, that permits to show the strong subadditivity inequality. As byproduct the strong convergence of the minimizing sequences (up to translations) is proved. We give an application to the energy functional I associated to the Schrödinger–Poisson equation in R3
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