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.
Benci, V., Luperi, L., Squassina, M., Generalized solutions of variational problems and applications, <<ADVANCES IN NONLINEAR ANALYSIS>>, 2020; (9): 124-147. [doi:10.1515/anona-2018-0146] [http://hdl.handle.net/10807/154879]
Generalized solutions of variational problems and applications
Squassina, Marco
2020
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.
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