%0 Journal Article %J Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337 %D 2016 %T Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I %A Giovanni Alberti %A Stefano Bianchini %A Laura Caravenna %B Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337 %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/35207 %1 35507 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-09-05T15:06:32Z No. of bitstreams: 1 1512.04863v2_Caravenna.pdf: 1192837 bytes, checksum: 15e7fc975989af0ea19654f4eafd84a7 (MD5) %R 10.1016/j.jde.2016.06.026 %0 Report %D 2016 %T Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II %A Giovanni Alberti %A Stefano Bianchini %A Laura Caravenna %G en %U http://urania.sissa.it/xmlui/handle/1963/35197 %1 35494 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-06-21T11:33:07Z No. of bitstreams: 1 file2ABCottobre2015.pdf: 486411 bytes, checksum: cbdd0bce26d338707c03a61c42ec725e (MD5) %0 Book Section %B AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406 %D 2014 %T Reduction on characteristics for continuous of a scalar balance law %A Giovanni Alberti %A Stefano Bianchini %A Laura Caravenna %K Method of characteristics %B AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406 %I SISSA %G en %U http://hdl.handle.net/1963/6562 %1 6516 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-04-03T07:48:04Z No. of bitstreams: 1 Alberti_11.pdf: 330968 bytes, checksum: a5f69e2a1d0afcfe139cf17ebcaf0f2d (MD5) %0 Journal Article %J Communications in Mathematical Physics 313 (2012) 1-33 %D 2012 %T SBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension %A Stefano Bianchini %A Laura Caravenna %B Communications in Mathematical Physics 313 (2012) 1-33 %I Springer %G en_US %U http://hdl.handle.net/1963/4091 %1 313 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-10-19T09:31:49Z\\r\\nNo. of bitstreams: 1\\r\\nBianchini_Caravenna_71M_2010.pdf: 591519 bytes, checksum: 388c1d8be60af95097574c718b4708b2 (MD5) %R 10.1007/s00220-012-1480-5 %0 Journal Article %J Mathematische Zeitschrift 268 (2011) 371-407 %D 2011 %T A proof of Sudakov theorem with strictly convex norms %A Laura Caravenna %X 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. %B Mathematische Zeitschrift 268 (2011) 371-407 %I Springer %G en_US %U http://hdl.handle.net/1963/2967 %1 1733 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-24T10:14:57Z\\r\\nNo. of bitstreams: 1\\r\\nsudStrConv.pdf: 432852 bytes, checksum: 0c4df310f125711293cef790005abc33 (MD5) %R 10.1007/s00209-010-0677-6 %0 Journal Article %J J. Funct. Anal. 258 (2010) 3604-3661 %D 2010 %T The disintegration of the Lebesgue measure on the faces of a convex function %A Laura Caravenna %A Sara Daneri %X

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.

%B J. Funct. Anal. 258 (2010) 3604-3661 %G en_US %U http://hdl.handle.net/1963/3622 %1 682 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-04-24T15:53:31Z\\nNo. of bitstreams: 1\\ndisconvCaravDaneri.pdf: 759110 bytes, checksum: e22e069339fc07c3bde1855b76e61d1e (MD5) %R 10.1016/j.jfa.2010.01.024 %0 Journal Article %J Comptes Rendus Mathematique 348 (2010) 613-618 %D 2010 %T On optimality of c-cyclically monotone transference plans %A Stefano Bianchini %A Laura Caravenna %X 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. %B Comptes Rendus Mathematique 348 (2010) 613-618 %I Elsevier %G en_US %U http://hdl.handle.net/1963/4023 %1 379 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-02T09:13:11Z\\nNo. of bitstreams: 1\\ncmonoNoteCRM.pdf: 154086 bytes, checksum: f2efc74ccfedd2e335ff99ff279b5cfd (MD5) %R 10.1016/j.crma.2010.03.022 %0 Thesis %D 2009 %T The Disintegration Theorem and Applications to Optimal Mass Transportation %A Laura Caravenna %I SISSA %G en %U http://hdl.handle.net/1963/5900 %1 5750 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-06-08T09:44:06Z\\nNo. of bitstreams: 1\\nPhDThesisCaravenna.pdf: 1700326 bytes, checksum: 9638dd5ad25fc3e1fb91399b1b12c293 (MD5) %0 Report %D 2009 %T An existence result for the Monge problem in R^n with norm cost %A Laura Caravenna %G en_US %U http://hdl.handle.net/1963/3647 %1 657 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-10T13:31:00Z\\nNo. of bitstreams: 1\\nMonge.sel.pdf: 1037029 bytes, checksum: 3f852fb5f7d74223ddee50818368c3f5 (MD5) %0 Journal Article %J Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458 %D 2009 %T On the extremality, uniqueness and optimality of transference plans %A Stefano Bianchini %A Laura Caravenna %X 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. %B Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458 %G en_US %U http://hdl.handle.net/1963/3692 %1 613 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-24T11:10:18Z\\nNo. of bitstreams: 1\\n46M2009.pdf: 485239 bytes, checksum: ebe15dc163dd6bdffcbe875730432b12 (MD5) %0 Journal Article %J J. Hyperbolic Differ. Equ. 5 (2008) 643-662 %D 2008 %T An entropy based Glimm-type functional %A Laura Caravenna %B J. Hyperbolic Differ. Equ. 5 (2008) 643-662 %I World Scientific %G en_US %U http://hdl.handle.net/1963/4051 %1 351 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-09T11:15:30Z\\nNo. of bitstreams: 1\\nglimm.potential.pdf: 405855 bytes, checksum: e2a5f3fed36ffe727c6d43240482aa6d (MD5) %R 10.1142/S0219891608001635