We focus on a very general problem in the theory of dynamic systems, namely that of studying measure differential inclusions with varying measures. The multifunction on the right hand side has compact non-necessarily convex values in a real Euclidean space and satisfies bounded variation hypotheses with respect to the Pompeiu excess (and not to the Hausdorff-Pompeiu distance, as usually in literature). This is possi- ble due to the use of interesting selection principles for excess bounded variation set-valued mappings. Conditions for the minimization of a generic functional with respect to a family of measures generated by equiregulated left-continuous, nondecreasing functions and to associated solu- tions of the differential inclusion driven by these measures are deduced, under constraints only on the initial point of the trajectory.

Valeria Marraffa, Luisa Di Piazza, & Bianca Satco (2020). Measure differential inclusions: existence results and minimum problems. SET-VALUED AND VARIATIONAL ANALYSIS [10.1007/s11228-020-00559-9].

Measure differential inclusions: existence results and minimum problems

Valeria Marraffa;Luisa Di Piazza;Bianca Satco
2020

Abstract

We focus on a very general problem in the theory of dynamic systems, namely that of studying measure differential inclusions with varying measures. The multifunction on the right hand side has compact non-necessarily convex values in a real Euclidean space and satisfies bounded variation hypotheses with respect to the Pompeiu excess (and not to the Hausdorff-Pompeiu distance, as usually in literature). This is possi- ble due to the use of interesting selection principles for excess bounded variation set-valued mappings. Conditions for the minimization of a generic functional with respect to a family of measures generated by equiregulated left-continuous, nondecreasing functions and to associated solu- tions of the differential inclusion driven by these measures are deduced, under constraints only on the initial point of the trajectory.
Settore MAT/05 - Analisi Matematica
Valeria Marraffa, Luisa Di Piazza, & Bianca Satco (2020). Measure differential inclusions: existence results and minimum problems. SET-VALUED AND VARIATIONAL ANALYSIS [10.1007/s11228-020-00559-9].
File in questo prodotto:
File Dimensione Formato  
Piazza2020_Article_MeasureDifferentialInclusionsE (1).pdf

accesso aperto

Tipologia: Versione Editoriale
Dimensione 439.98 kB
Formato Adobe PDF
439.98 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/433312
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 3
social impact