caa a22 4500 445843659 CHVBK 20180317145352.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s00526-011-0392-0 doi (NATIONALLICENCE)springer-10.1007/s00526-011-0392-0 Convexity and semiconvexity along vector fields [Elektronische Daten] [Martino Bardi, Federica Dragoni] Given a family of vector fields we introduce a notion of convexity and of semiconvexity of a function along the trajectories of the fields and give infinitesimal characterizations in terms of inequalities in viscosity sense for the matrix of second derivatives with respect to the fields. We also prove that such functions are Lipschitz continuous with respect to the Carnot-Carathéodory distance associated to the family of fields and have a bounded gradient in the directions of the fields. This extends to Carnot-Carathéodory metric spaces several results for the Heisenberg group and Carnot groups obtained by a number of authors. Springer-Verlag, 2011 Bardi Martino Dipartimento di Matematica P. e A., Università di Padova, via Trieste 63, 35121, Padova, Italy aut Dragoni Federica Dipartimento di Matematica P. e A., Università di Padova, via Trieste 63, 35121, Padova, Italy aut Calculus of Variations and Partial Differential Equations Springer-Verlag 42/3-4(2011-11-01), 405-427 0944-2669 42:3-4<405 2011 42 526 https://doi.org/10.1007/s00526-011-0392-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-011-0392-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bardi Martino Dipartimento di Matematica P. e A., Università di Padova, via Trieste 63, 35121, Padova, Italy aut NATIONALLICENCE 700 1- Dragoni Federica Dipartimento di Matematica P. e A., Università di Padova, via Trieste 63, 35121, Padova, Italy aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 42/3-4(2011-11-01), 405-427 0944-2669 42:3-4<405 2011 42 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer