TY - JOUR T1 - Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I JF - Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337 Y1 - 2016 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Laura Caravenna PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/35207 U1 - 35507 U2 - Mathematics ER - TY - RPRT T1 - Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II Y1 - 2016 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Laura Caravenna UR - http://urania.sissa.it/xmlui/handle/1963/35197 U1 - 35494 U2 - Mathematics ER - TY - CHAP T1 - Reduction on characteristics for continuous of a scalar balance law T2 - AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406 Y1 - 2014 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Laura Caravenna KW - Method of characteristics JF - AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406 PB - SISSA UR - http://hdl.handle.net/1963/6562 U1 - 6516 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - SBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension JF - Communications in Mathematical Physics 313 (2012) 1-33 Y1 - 2012 A1 - Stefano Bianchini A1 - Laura Caravenna PB - Springer UR - http://hdl.handle.net/1963/4091 U1 - 313 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A proof of Sudakov theorem with strictly convex norms JF - Mathematische Zeitschrift 268 (2011) 371-407 Y1 - 2011 A1 - Laura Caravenna AB - We establish a solution to the Monge problem in Rn, with an asymmetric, strictly convex norm cost function, when the initial measure is absolutely continuous. We focus on the strategy, based on disintegration of measures, initially proposed by Sudakov. As known, there is a gap to fill. The missing step is completed when the unit ball is strictly convex, but not necessarily differentiable nor uniformly convex. The key disintegration is achieved following a similar proof for a variational problem. PB - Springer UR - http://hdl.handle.net/1963/2967 U1 - 1733 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The disintegration of the Lebesgue measure on the faces of a convex function JF - J. Funct. Anal. 258 (2010) 3604-3661 Y1 - 2010 A1 - Laura Caravenna A1 - Sara Daneri AB -

We consider the disintegration of the Lebesgue measure on the graph of a convex function f:\\\\Rn-> \\\\R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure of the k-dimensional face on which it is concentrated. The remarkable fact is that a priori the directions of the faces are just Borel and no Lipschitz regularity is known. Notwithstanding that, we also prove that a Green-Gauss formula for these directions holds on special sets.

UR - http://hdl.handle.net/1963/3622 U1 - 682 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On optimality of c-cyclically monotone transference plans JF - Comptes Rendus Mathematique 348 (2010) 613-618 Y1 - 2010 A1 - Stefano Bianchini A1 - Laura Caravenna AB - Abstract. This note deals with the equivalence between the optimality of a transport plan for the Monge-Kantorovich problem and the condition of c-cyclical monotonicity, as an outcome of the construction in [7]. We emphasize the measurability assumption on the hidden structure of linear preorder, applied also to extremality and uniqueness problems. Resume. Dans la presente note nous decrivons brievement la construction introduite dans [7] a propos de l\\\'equivalence entre l\\\'optimalite d\\\'un plan de transport pour le probleme de Monge-Kantorovich et la condition de monotonie c-cyclique ainsi que d\\\'autres sujets que cela nous amene a aborder. Nous souhaitons mettre en evidence l\\\'hypothese de mesurabilite sur la structure sous-jacente de pre-ordre lineaire. PB - Elsevier UR - http://hdl.handle.net/1963/4023 U1 - 379 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - The Disintegration Theorem and Applications to Optimal Mass Transportation Y1 - 2009 A1 - Laura Caravenna PB - SISSA UR - http://hdl.handle.net/1963/5900 U1 - 5750 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - An existence result for the Monge problem in R^n with norm cost Y1 - 2009 A1 - Laura Caravenna UR - http://hdl.handle.net/1963/3647 U1 - 657 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the extremality, uniqueness and optimality of transference plans JF - Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458 Y1 - 2009 A1 - Stefano Bianchini A1 - Laura Caravenna AB - We consider the following standard problems appearing in optimal mass transportation theory: when a transference plan is extremal; when a transference plan is the unique transference plan concentrated on a set A,; when a transference plan is optimal. UR - http://hdl.handle.net/1963/3692 U1 - 613 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An entropy based Glimm-type functional JF - J. Hyperbolic Differ. Equ. 5 (2008) 643-662 Y1 - 2008 A1 - Laura Caravenna PB - World Scientific UR - http://hdl.handle.net/1963/4051 U1 - 351 U2 - Mathematics U3 - Functional Analysis and Applications ER -