caa a22 4500 477091555 CHVBK 20180405111516.0 cr unu---uuuuu 170330e19961201xx s 000 0 eng 10.1007/BF01193832 doi (NATIONALLICENCE)springer-10.1007/BF01193832 Measure properties of the set of initial data yielding non uniqueness for a class of differential inclusions [Elektronische Daten] [Paolo Caldiroli, Giulia Treu] We study uniqueness property for the Cauchy problemx′∈ϖV(x), x(0)=ξ, whereV∶R n→R is a locally Lipschitz continuous, quasiconvex function (i.e. the sublevel sets {V≤c} are convex) and ϖV(x) is the generalized gradient ofV atx. We prove that if 0∉ϖV(x) forV(x)≥b, then the set of initial data ξ∈{V=b} yielding non uniqueness of solution in a geometric sense has (n−1)-dimensional Hausdorff measure zero in {V=b}. Birkhäuser Verlag, 1996 Caldiroli Paolo Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2-4, 34013, Trieste, Italy aut Treu Giulia Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 204, 33100, Udine, Italy aut Nonlinear Differential Equations and Applications NoDEA Birkhäuser-Verlag 3/4(1996-12-01), 499-507 1021-9722 3:4<499 1996 3 30 https://doi.org/10.1007/BF01193832 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01193832 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Caldiroli Paolo Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2-4, 34013, Trieste, Italy aut NATIONALLICENCE 700 1- Treu Giulia Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 204, 33100, Udine, Italy aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Birkhäuser-Verlag 3/4(1996-12-01), 499-507 1021-9722 3:4<499 1996 3 30 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer