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 - 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 - 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 -