@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}
}
@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 = {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}
}