Generalized solutions of variational problems and applications

Abstract

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

23 pages. arXiv admin note: text overlap with arXiv:1707.09265