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 (2021). 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
2021-01-01

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.
2021
Settore MAT/05 - Analisi Matematica
Valeria Marraffa, Luisa Di Piazza, Bianca Satco (2021). Measure differential inclusions: existence results and minimum problems. SET-VALUED AND VARIATIONAL ANALYSIS [10.1007/s11228-020-00559-9].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/433312
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