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 - JOUR
T1 - Existence and uniqueness of the gradient flow of the Entropy in the space of probability measures
Y1 - 2014
A1 - Stefano Bianchini
A1 - Alexander Dabrowski
AB - After a brief introduction on gradient flows in metric spaces and on geodesically convex functionals, we give an account of the proof (following the outline of [3, 7]) of the existence and uniqueness of the gradient flow of the Entropy in the space of Borel probability measures over a compact geodesic metric space with Ricci curvature bounded from below.
PB - EUT Edizioni Universita di Trieste
UR - http://urania.sissa.it/xmlui/handle/1963/34693
N1 - This paper resumes the main part of the Bachelor thesis of the second author, discussed
in 2013 at the University of Trieste.
U1 - 34907
U2 - Mathematics
U4 - 1
ER -
TY - JOUR
T1 - An Estimate on the Flow Generated by Monotone Operators
JF - Communications in Partial Differential Equations 36 (2011) 777-796
Y1 - 2011
A1 - Stefano Bianchini
A1 - Matteo Gloyer
PB - Taylor & Francis
UR - http://hdl.handle.net/1963/3646
U1 - 658
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Estimates on path functionals over Wasserstein Spaces
JF - SIAM J. Math. Anal. 42 (2010) 1179-1217
Y1 - 2010
A1 - Stefano Bianchini
A1 - Alessio Brancolini
AB - In this paper we consider the class a functionals (introduced in [Brancolini, Buttazzo, and Santambrogio, J. Eur. Math. Soc. (JEMS), 8 (2006), pp. 415-434] $\\\\mathcal{G}_{r,p}$ defined on Lipschitz curves $\\\\gamma$ valued in the $p$-Wasserstein space. The problem considered is the following: given a measure $\\\\mu$, give conditions in order to assure the existence of a curve $\\\\gamma$ such that $\\\\gamma(0)=\\\\mu$, $\\\\gamma(1)=\\\\delta_{x_0}$, and $\\\\mathcal{G}_{r,p}(\\\\gamma)<+\\\\infty$. To this end, new estimates on $\\\\mathcal{G}_{r,p}(\\\\mu)$ are given, and a notion of dimension of a measure (called path dimension) is introduced: the path dimension specifies the values of the parameters $(r,p)$ for which the answer to the previous reachability problem is positive. Finally, we compare the path dimension with other known dimensions.
UR - http://hdl.handle.net/1963/3583
U1 - 717
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - On the Euler-Lagrange equation for a variational problem : the general case II
JF - Math. Z. 265 (2010) 889-923
Y1 - 2010
A1 - Stefano Bianchini
A1 - Matteo Gloyer
UR - http://hdl.handle.net/1963/2551
U1 - 1568
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 - On the Euler-Lagrange equation for a variational problem
JF - Discrete Contin. Dynam. Systems A 17 (2007) 449-480
Y1 - 2007
A1 - Stefano Bianchini
UR - http://hdl.handle.net/1963/1792
U1 - 2752
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Extremal faces of the range of a vector measure and a theorem of Lyapunov
JF - J. Math. Anal. Appl. 231 (1999) 301-318
Y1 - 1999
A1 - Stefano Bianchini
PB - Elsevier
UR - http://hdl.handle.net/1963/3370
U1 - 960
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -