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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Scaling properties of functionals and existence of constrained minimizers

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Bellazzini, Jacopo [1] ; Siciliano, Gaetano [2]
Total Authors: 2
[1] Univ Sassari, I-07100 Sassari - Italy
[2] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo - Brazil
Total Affiliations: 2
Document type: Journal article
Source: JOURNAL OF FUNCTIONAL ANALYSIS; v. 261, n. 9, p. 2486-2507, NOV 1 2011.
Web of Science Citations: 26

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 Schrodinger-Poisson equation in IR(3) i psi(t) + Delta psi - (|x|(-1) {*} |psi|(2))psi + |psi|(p-2)psi = 0 when 2 < p < 3. In particular we prove that I achieves its minimum on the constraint [u is an element of H(1) (R(3)): parallel to u parallel to(2) = rho] for every sufficiently small rho > 0. In this way we recover the case studied in Sanchez and Soler (2004) {[}20] for p = 8/3 and we complete the case studied by the authors for 3 < p < 10/3 in Bellazzini and Siciliano (2011) {[}4]. (C) 2011 Elsevier Inc. All rights reserved. (AU)

FAPESP's process: 11/01081-9 - Geometric variational problems and PDEs
Grantee:Paolo Piccione
Support type: Research Grants - Visiting Researcher Grant - International