Generalized solutions of variational problems and applications

Marco Squassina, Vieri Benci, Lorenzo Luperi

Risultato della ricerca: Contributo in rivistaArticolo in rivista

Abstract

Ultrafunctions are a particular class of generalized functions defined on a hyperreal field ℝ∗ ⊃ ℝ that allow to solve variational problems with no classical solutions. We recall the construction of ultrafunctions and we study the relationships between these generalized solutions and classical minimizing sequences. Finally, we study some examples to highlight the potential of this approach.
Lingua originaleEnglish
pagine (da-a)124-147
Numero di pagine24
RivistaAdvances in Nonlinear Analysis
Stato di pubblicazionePubblicato - 2020

Keywords

  • nonstandard analysis

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