### Luigi Ambrosio - Selected publications#

BOOKS

[1] Functions of Bounded Variation and Free Discontinuity Problems.
(with N.Fusco and D.Pallara) Oxford University Press, 2000.

[2] Gradient flows in metric spaces and in the space of Probability measures. (with N.Gigli and G.Savarè)
Lectures in Mathematics ETH Zurich, Birkhäuser, 2005, second edition in 2008.

PAPERS

[1] Existence theory for a new class of variational problems, Archive for Rational Mechanics Analysis, 111, 291-322, 1990.

[2] Metric space valued functions of bounded variation,
Annali della Scuola Normale Superiore, 17, 439-478, 1990.

[3] Approximation of functionals depending on jumps by elliptic functionals via $\Gamma$-convergence (with V.M.Tortorelli),
Communications on Pure and Applied Mathematics, 43, 999-1036, 1990.

[4] A level set approach for the evolution of surfaces of any codimension
(with H.M.Soner), J. Diff. Geom. 43 (1996), 693-737.

[5] Partial regularity of free discontinuity sets II (with N.Fusco, D.Pallara),
Ann. Scuola Norm. Sup. Pisa, 24 (1997), 39-62.

[6] Currents in metric spaces. (with B.Kirchheim) Acta Mathematica, 185 (2000), 1-80.

[7] Transport equation and Cauchy probem for $BV$ vector fields. Inventiones Mathematicae, {\bf 158} (2004), 227-260.

[8] Calculus and heat flow in metric measure spaces and applications to spaces with ricci bounds from below.
(with N.Gigli, G.Savarè) 2011, to appear on Inventiones Mathematicae, 100pp.