# Generalized solutions of variational problems and applications

created by squassina on 27 Jun 2018

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Submitted Paper

Inserted: 27 jun 2018
Last Updated: 27 jun 2018

Year: 2018

Abstract:

Ultrafunctions are a particular class of generalized functions defined on a hyperreal field $\mathbb{R}^{*}\supset\mathbb{R}$ 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.