@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 {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 {2014,
	title = {On the Lp-differentiability of certain classes of functions},
	number = {Revista Matematica Iberoamericana;Volume 30; issue 1; pp. 349-367;},
	year = {2014},
	publisher = {European Mathematical Society},
	abstract = {We prove the Lp-differentiability at almost every point for convolution products on ℝd of the form K*μ, where μ is bounded measure and K is a homogeneous kernel of degree 1-d. From this result we derive the Lp-differentiability for vector fields on R d whose curl and divergence are measures, and also for vector fields with bounded deformation.},
	doi = {10.4171/rmi/782},
	url = {http://urania.sissa.it/xmlui/handle/1963/34695},
	author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa}
}
@inbook {2013,
	title = {Reduction on characteristics for continuous of a scalar balance law},
	booktitle = {AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406},
	number = {AIMS Series on Applied Mathematics},
	year = {2014},
	publisher = {SISSA},
	organization = {SISSA},
	keywords = {Method of characteristics},
	url = {http://hdl.handle.net/1963/6562},
	author = {Giovanni Alberti and Stefano Bianchini and Laura Caravenna}
}
@article {2014,
	title = {A uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday},
	number = {Journal of the European Mathematical Society;Volume 16; issue 2; pp. 201-234;},
	year = {2014},
	publisher = {European Mathematical Society; Springer Verlag},
	abstract = {We characterize the autonomous, divergence-free vector fields b on the plane such that the Cauchy problem for the continuity equation ∂tu +div(bu) = 0 admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential f associated to b. As a corollary we obtain uniqueness under the assumption that the curl of b is a measure. This result can be extended to certain nonautonomous vector fields b with bounded divergence.},
	doi = {10.4171/JEMS/431},
	url = {http://urania.sissa.it/xmlui/handle/1963/34692},
	author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa}
}
@article {2011,
	title = {Quasistatic evolution of sessile drops and contact angle hysteresis},
	journal = {Arch. Rational Mech. Anal. 202 (2011) 295-348},
	year = {2011},
	publisher = {Springer},
	abstract = {We consider the classical model of capillarity coupled with a rate-independent dissipation mechanism due to frictional forces acting on the contact line, and prove the existence of quasistatic evolutions with prescribed initial configuration. We also discuss in detail some explicit solutions to show that the model does account for contact angle hysteresis, and to compare its predictions with experimental observations.},
	doi = {10.1007/s00205-011-0427-x},
	url = {http://hdl.handle.net/1963/4912},
	author = {Giovanni Alberti and Antonio DeSimone}
}
@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 {2011,
	title = {A uniqueness result for the continuity equation in two dimensions},
	number = {SISSA;52/2011/M},
	year = {2011},
	institution = {SISSA},
	url = {http://hdl.handle.net/1963/4663},
	author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa}
}
@article {2005,
	title = {Wetting of rough surfaces: a homogenization approach},
	journal = {Proc. R. Soc. Lon. Ser. A 461 (2005) 79-97},
	number = {SISSA;75/2004/M},
	year = {2005},
	abstract = {The contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness-induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact angle is associated with the solution of two cell problems, giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapor phase. Our results are valid for both chemically heterogeneous and homogeneous surfaces. In the latter case, a very transparent structure emerges from the variational\\napproach: the classical laws of Wenzel and Cassie-Baxter give bounds for the optimal energy, and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case, to the largest one in the hydrophilic case.},
	doi = {10.1098/rspa.2004.1364},
	url = {http://hdl.handle.net/1963/2253},
	author = {Antonio DeSimone and Giovanni Alberti}
}
@article {2003,
	title = {The calibration method for the Mumford-Shah functional and free-discontinuity problems},
	journal = {Calc. Var. Partial Differential Equations 16 (2003) 299-333},
	number = {SISSA;35/2001/M},
	year = {2003},
	publisher = {Springer},
	abstract = {We present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results.},
	doi = {10.1007/s005260100152},
	url = {http://hdl.handle.net/1963/3051},
	author = {Giovanni Alberti and Guy Bouchitte and Gianni Dal Maso}
}
@article {1999,
	title = {The calibration method for the Mumford-Shah functional},
	journal = {C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 3, 249-254},
	number = {SISSA;21/99/M},
	year = {1999},
	publisher = {Elsevier},
	abstract = {In this Note we adapt the calibration method to functionals of Mumford-Shah type, and provide a criterion (Theorem 1) to verify that a given function is energy minimizing. Among other applications, we use this criterion to show that certain triple-junction configurations are minimizing (Example 3).},
	doi = {10.1016/S0764-4442(00)88602-4},
	url = {http://hdl.handle.net/1963/1235},
	author = {Giovanni Alberti and Guy Bouchitte and Gianni Dal Maso}
}
