@article {2016,
title = {Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II},
number = {SISSA;32/2016/MATE},
year = {2016},
url = {http://urania.sissa.it/xmlui/handle/1963/35197},
author = {Giovanni Alberti and Stefano Bianchini and Laura Caravenna}
}
@article {2016,
title = {Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I},
journal = {Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337},
number = {Journal of Differential Equations;261},
year = {2016},
publisher = {Elsevier},
doi = {10.1016/j.jde.2016.06.026},
url = {http://urania.sissa.it/xmlui/handle/1963/35207},
author = {Giovanni Alberti and Stefano Bianchini and Laura Caravenna}
}
@article {2014,
title = {Existence and uniqueness of the gradient flow of the Entropy in the space of probability measures},
number = {Rendiconti dell{\textquoteright}Istituto di Matematica dell{\textquoteright}Universita di Trieste;Volume 46; issue 1; pp. 43-70;},
year = {2014},
note = {This paper resumes the main part of the Bachelor thesis of the second author, discussed
in 2013 at the University of Trieste.},
publisher = {EUT Edizioni Universita di Trieste},
abstract = {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.},
url = {http://urania.sissa.it/xmlui/handle/1963/34693},
author = {Stefano Bianchini and Alexander Dabrowski}
}
@article {2011,
title = {An Estimate on the Flow Generated by Monotone Operators},
journal = {Communications in Partial Differential Equations 36 (2011) 777-796},
number = {SISSA;29/2009/M},
year = {2011},
publisher = {Taylor \& Francis},
doi = {10.1080/03605302.2010.534224},
url = {http://hdl.handle.net/1963/3646},
author = {Stefano Bianchini and Matteo Gloyer}
}
@article {2010,
title = {Estimates on path functionals over Wasserstein Spaces},
journal = {SIAM J. Math. Anal. 42 (2010) 1179-1217},
number = {SISSA;11/2009/M},
year = {2010},
abstract = {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.},
doi = {10.1137/100782693},
url = {http://hdl.handle.net/1963/3583},
author = {Stefano Bianchini and Alessio Brancolini}
}
@article {2010,
title = {On the Euler-Lagrange equation for a variational problem : the general case II},
journal = {Math. Z. 265 (2010) 889-923},
number = {SISSA;75/2007/M},
year = {2010},
doi = {10.1007/s00209-009-0547-2},
url = {http://hdl.handle.net/1963/2551},
author = {Stefano Bianchini and Matteo Gloyer}
}
@article {2009,
title = {On the extremality, uniqueness and optimality of transference plans},
journal = {Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458},
number = {SISSA;46/2009/M},
year = {2009},
abstract = {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.},
url = {http://hdl.handle.net/1963/3692},
author = {Stefano Bianchini and Laura Caravenna}
}
@article {2007,
title = {On the Euler-Lagrange equation for a variational problem},
journal = {Discrete Contin. Dynam. Systems A 17 (2007) 449-480},
number = {SISSA;95/2005/M},
year = {2007},
url = {http://hdl.handle.net/1963/1792},
author = {Stefano Bianchini}
}
@article {1999,
title = {Extremal faces of the range of a vector measure and a theorem of Lyapunov},
journal = {J. Math. Anal. Appl. 231 (1999) 301-318},
number = {SISSA;4/98/M},
year = {1999},
publisher = {Elsevier},
doi = {10.1006/jmaa.1998.6260},
url = {http://hdl.handle.net/1963/3370},
author = {Stefano Bianchini}
}