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Adjoint functions to boundary solutions of differential inclusions and smoothness of barrier solutions on semipermeable surfaces

100%

Leśniewski A.

2007

tom Vol. 40, nr 1

107-114

The problem of existence of adjoint functions to boundary solutions is considered – it depends on the geometry of the attained set at the end point. This is applied to prove the smoothness of boundary solutions in the case of strictly convex right-hand side of di.erential inclusion which in turn permitts to show the smoothness of barrier solutions on semipermeable surfaces.

The Demyanov metric and measurable multifunctions

100%

Leśniewski A.

2010

tom Vol. 33

61-65

We present in this paper measurability multifunctions in the family of all convex, bounded sets which need not be closed. The Demyanov metric is discussed.

Autonomous differential inclusion sharing the families of trajectories

63%

Leśniewski A. , Rzeżuchowski T.

2006

tom Vol. 39, nr 2

347-356

We give a sufficient condition for equality of sets of trajectories of two differential inclusions with right-hand sides Borel measurable with respect to the state variable, not necessarily bounded and possibly containing the origin.