Scaling properties of functionals and existence of constrained minimizers |
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Authors: | Jacopo Bellazzini Gaetano Siciliano |
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Institution: | a Università di Sassari, via Piandanna 4, 07100 Sassari, Italy b Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-090, São Paulo, Brazil |
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Abstract: | 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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Keywords: | Constrained minimization Subadditivity inequality Schrö dinger-Poisson equations Standing waves |
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