@article {2016,
	title = {On the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension},
	year = {2016},
	institution = {SISSA},
	abstract = {<p>We prove that if $u$ is the entropy solution to a scalar conservation law in one space dimension, then the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This result is a consequence of a detailed analysis of the structure of the characteristics. In particular the characteristic curves are segments outside a countably 1-rectifiable set and the left and right traces of the solution exist in a $C^0$-sense up to the degeneracy due to the segments where $f{\textquoteright}{\textquoteright}=0$. We prove also that the initial data is taken in a suitably strong sense and we give some counterexamples which show that these results are sharp.</p>},
	url = {http://urania.sissa.it/xmlui/handle/1963/35209},
	author = {Stefano Bianchini and Elio Marconi}
}
@article {2014,
	title = {SBV Regularity of Systems of Conservation Laws and Hamilton{\textendash}Jacobi Equations},
	number = {Journal of Mathematical Sciences;Volume 201; issue 6; pp. 733-745;},
	year = {2014},
	publisher = {Springer},
	abstract = {We review the SBV regularity for solutions to hyperbolic systems of conservation laws and Hamilton-Jacobi equations. We give an overview of the techniques involved in the proof, and a collection of related problems concludes the paper.},
	doi = {10.1007/s10958-014-2022-9},
	url = {http://urania.sissa.it/xmlui/handle/1963/34691},
	author = {Stefano Bianchini}
}
@article {2014,
	title = {Steady nearly incompressible vector  elds in 2D: chain rule and renormalization},
	year = {2014},
	institution = {SISSA},
	author = {Stefano Bianchini and N.A. Gusev}
}
@article {2014,
	title = {Structure of entropy solutions to general scalar conservation laws in one space dimension},
	journal = {Journal of Mathematical Analysis and Applications},
	volume = {428},
	number = {SISSA;11/2014/MATE},
	year = {2014},
	month = {08/2015},
	pages = {356-386},
	publisher = {SISSA},
	chapter = {356},
	doi = {https://doi.org/10.1016/j.jmaa.2015.03.006},
	url = {https://www.sciencedirect.com/science/article/pii/S0022247X15002218},
	author = {Stefano Bianchini and Lei Yu}
}
@article {2013,
	title = {On Sudakov{\textquoteright}s type decomposition of transference plans with norm costs},
	number = {SISSA;51/2013/MATE},
	year = {2013},
	institution = {SISSA},
	url = {http://hdl.handle.net/1963/7206},
	author = {Stefano Bianchini and Sara Daneri}
}
@article {2012,
	title = {SBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension},
	journal = {Communications in Mathematical Physics 313 (2012) 1-33},
	number = {SISSA;71/2010/M},
	year = {2012},
	publisher = {Springer},
	doi = {10.1007/s00220-012-1480-5},
	url = {http://hdl.handle.net/1963/4091},
	author = {Stefano Bianchini and Laura Caravenna}
}
@article {2011,
	title = {SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x)},
	journal = {Siam Journal on Mathematical Analysis},
	volume = {44},
	number = {SISSA;13/2011/M},
	year = {2012},
	pages = {2179-2203},
	publisher = {SISSA},
	doi = {10.1137/110827272},
	url = {http://hdl.handle.net/20.500.11767/14066},
	author = {Stefano Bianchini and Daniela Tonon}
}
@article {2012,
	title = {SBV regularity of genuinely nonlinear hyperbolic systems of conservation laws in one space dimension},
	journal = {Acta Mathematica Scientia, Volume 32, Issue 1, January 2012, Pages 380-388},
	year = {2012},
	publisher = {Elsevier},
	abstract = {The problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered. An overview of the techniques involved in the proof is given, and a collection of related problems concludes the paper. Key words hyperbolic systems; conservation laws; SBV; regularity},
	keywords = {Hyperbolic systems},
	doi = {10.1016/S0252-9602(12)60024-1},
	url = {http://hdl.handle.net/1963/6535},
	author = {Stefano Bianchini}
}
@article {bianchini2012sbv,
	title = {SBV-like regularity for general hyperbolic systems of conservation laws in one space dimension},
	journal = {Rend. Istit. Mat. Univ. Trieste},
	volume = {44},
	year = {2012},
	pages = {439{\textendash}472},
	author = {Stefano Bianchini and Lei Yu}
}
@article {2012,
	title = {SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian},
	journal = {Journal of Mathematical Analysis and Applications},
	volume = {391},
	number = {SISSA;45/2011/M},
	year = {2012},
	pages = {190-208},
	publisher = {SISSA},
	doi = {10.1016/j.jmaa.2012.02.017},
	url = {http://hdl.handle.net/20.500.11767/13909},
	author = {Stefano Bianchini and Daniela Tonon}
}
@article {2011,
	title = {SBV regularity for Hamilton-Jacobi equations in R^n},
	journal = {Arch. Rational Mech. Anal. 200 (2011) 1003-1021},
	number = {arXiv:1002.4087;},
	year = {2011},
	publisher = {Springer},
	abstract = {<p>In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in}\quad \Omega\subset \mathbb{R}\times \mathbb{R}^{n} . $$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb{R}^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.</p>},
	doi = {10.1007/s00205-010-0381-z},
	url = {http://hdl.handle.net/1963/4911},
	author = {Stefano Bianchini and Camillo De Lellis and Roger Robyr}
}
@article {2011,
	title = {Structure of level sets and Sard-type properties of Lipschitz maps},
	number = {SISSA;51/2011/M},
	year = {2011},
	institution = {SISSA},
	url = {http://hdl.handle.net/1963/4657},
	author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa}
}
@article {2002,
	title = {On the Stability of the Standard Riemann Semigroup},
	journal = {P. Am. Math. Soc., 2002, 130, 1961},
	number = {SISSA;71/00/M},
	year = {2002},
	publisher = {SISSA Library},
	url = {http://hdl.handle.net/1963/1528},
	author = {Stefano Bianchini and Rinaldo M. Colombo}
}
@article {2001,
	title = {Stability of L-infinity solutions for hyperbolic systems with coinciding shocks and rarefactions},
	journal = {Siam J. Math. Anal., 2001, 33, 959},
	number = {SISSA;65/00/M},
	year = {2001},
	publisher = {SISSA Library},
	abstract = {We consider a hyperbolic system of conservation laws u_t + f(u)_x = 0 and u(0,\\\\cdot) = u_0, where each characteristic field is either linearly degenerate or genuinely nonlinear. Under the assumption of coinciding shock and rarefaction curves and the existence of a set of Riemann coordinates $w$, we prove that there exists a semigroup of solutions $u(t) = \\\\mathcal{S}_t u_0$, defined on initial data $u_0 \\\\in L^\\\\infty$. The semigroup $\\\\mathcal{S}$ is continuous w.r.t. time and the initial data $u_0$ in the $L^1_{\\\\text{loc}}$ topology. Moreover $\\\\mathcal{S}$ is unique and its trajectories are obtained as limits of wave front tracking approximations.},
	doi = {10.1137/S0036141000377900},
	url = {http://hdl.handle.net/1963/1523},
	author = {Stefano Bianchini}
}
@article {2000,
	title = {The semigroup generated by a Temple class system with non-convex flux function},
	journal = {Differential Integral Equations 13 (2000) 1529-1550},
	number = {SISSA;107/98/M},
	year = {2000},
	publisher = {Khayyam Publishing},
	abstract = {We consider the Cauchy problem for a nonlinear n {\texttimes} n system of conservation laws of Temple class, i.e. with coinciding shock and rarefaction curves and with a coordinate system made of Riemann invariants. Without any assumption on the convexity of the flux function, we prove the existence of a semigroup made of weak solutions of the equations and depending Lipschitz continuously on the initial data with bounded total variation.},
	url = {http://hdl.handle.net/1963/3221},
	author = {Stefano Bianchini}
}
@article {2000,
	title = {On the shift differentiability of the flow generated by a hyperbolic system of conservation laws},
	journal = {Discrete Contin. Dynam. Systems 6 (2000), no. 2, 329-350},
	number = {SISSA;60/99/M},
	year = {2000},
	publisher = {American Institute of Mathematical Sciences},
	doi = {10.3934/dcds.2000.6.329},
	url = {http://hdl.handle.net/1963/1274},
	author = {Stefano Bianchini}
}
