M. Colombo, M. Gobbino:
Slow time behavior of the semidiscrete Perona-Malik scheme in dimension one
SIAM J. Math. Anal. (Accepted Paper) p. 42, 2010
M. Colombo, M. Gobbino:
Passing to the limit in maximal slope curves: from a regularized Perona-Malik equation to the total variation flow
Math. Models Methods Appl. Sci. (Accepted Paper) 2011
E. Bardelli, M. Colombo, A. C. G. Mennucci, A. Yezzi:
Multiple Object Tracking via Prediction and Filtering with a Sobolev-type Metric on Curves
Fifth Workshop on Non-Rigid Shape Analysis and Deformable Image Alignment (NORDIA'12) p. 10, 2012
M. Colombo, A. Figalli:
Regularity results for very degenerate elliptic equations
J. Math. Pures Appl. (Accepted Paper) 2012
L. Ambrosio, M. Colombo, G. De Philippis, A. Figalli:
A global existence result for the semigeostrophic equations in three
dimensional convex domains
Discrete Contin. Dyn. Syst. (Accepted Paper) 2012
L. Ambrosio, M. Colombo, G. De Philippis, A. Figalli:
Existence of Eulerian solutions to the semigeostrophic equations in
physical space: the 2-dimensional periodic case
Comm. Partial Differential Equations (Accepted Paper) 2012
L. Ambrosio, M. Colombo, S. Di Marino:
Sobolev spaces in metric measure spaces: reflexivity and lower
semicontinuity of slope
Advanced Studies in Pure Mathematics: "Variational methods for evolving objects" (Accepted Paper) Vol. 67, p. 1-58, 2012
M. Colombo, S. Di Marino:
Equality between Monge and Kantorovich multimarginal problems with Coulomb cost
Ann. Mat. Pura Appl. (Accepted Paper) p. 14, 2013
M. Colombo, A. Figalli:
An excess-decay result for a class of degenerate elliptic equations
Discrete Contin. Dyn. Syst. (Accepted Paper) 2013
M. Colombo, L. De Pascale, S. Di Marino:
Multimarginal Optimal Transpor Maps for 1-Dimensional Repulsive Costs
Canad. J. Math. (Accepted Paper) p. 18, 2013
F. Cagnetti, M. Colombo, G. De Philippis, F. Maggi:
Rigidity of equality cases in Steiner's perimeter inequality
Anal. PDE (Accepted Paper) 2013
F. Cagnetti, M. Colombo, G. De Philippis, F. Maggi:
Essential connectedness and the rigidity problem for Gaussian
symmetrization
J. Eur. Math. Soc. (Accepted Paper) 2013
M. Colombo, E. Indrei:
Obstructions to regularity in the classical Monge problem
Math. Res. Lett. (Accepted Paper) 2014
M. Colombo, G. Crippa, S. Spirito:
Renormalized solutions to the continuity equation with an integrable damping term
Calc. Var. PDE (Accepted Paper) 2015
L. Ambrosio, M. Colombo, A. Figalli:
Existence and uniqueness of maximal regular flows for non-smooth vector fields
Arch. Ration. Mech. Anal. (Accepted Paper) 2015
M. Colombo:
Flows of non-smooth vector fields and degenerate elliptic equations
(Phd Thesis) 2015
P. Baroni, M. Colombo, G. Mingione:
Harnack inequalities for double phase functionals
Nonlinear Analysis Vol. 121, p. 206-222, 2015
M. Colombo, F. Stra:
Counterexamples in multimarginal optimal transport with Coulomb cost and
spherically symmetric data
Math. Models Methods Appl. Sci. (Accepted Paper) 2015
A. Braides, M. Colombo, M. Gobbino, M. Solci:
Minimizing movements along a sequence of functionals and curves of maximal slope
C. R. Acad. Sci. Paris, Ser. I Vol. 354, N. 7, p. 685-689, 2016
M. Colombo, F. Maggi:
Existence and almost everywhere regularity of isoperimetric clusters for fractional perimeters
Nonlinear Analysis (Accepted Paper) 2016
P. Baroni, M. Colombo, G. Mingione:
Non-autonomous functionals, borderline cases and related function classes
St. Petersburg Math. J. Vol. 27, N. 3, p. 347-379, 2016
S. Bianchini, M. Colombo, G. Crippa, L. V. Spinolo:
Optimality of integrability estimates for advection-diffusion equations
(Submitted Paper) 2017
M. Colombo, A. Figalli, Y. Jhaveri:
Lipschitz changes of variables between perturbations of log-concave measures
Ann. Sc. Norm. Super. Pisa Cl. Sci. (Accepted Paper) 2017
L. Ambrosio, M. Colombo, A. Figalli:
On the Lagrangian structure of transport equations: the Vlasov-Poisson system
Duke Math. J. (Accepted Paper) 2017
M. Colombo, A. De Rosa, A. Marchese, S. Stuvard:
On the lower semicontinuous envelope of functionals defined on polyhedral chains
Nonlinear Analysis Vol. 163C, p. 201-215, 2017
M. Colombo, L. Spolaor:
Quantitative estimate on singularities in isoperimetric clusters
CAG (Accepted Paper) 2017
M. Colombo, G. Crippa, L. V. Spinolo:
On the singular local limit for conservation laws with nonlocal fluxes
(Preprint) 2017
M. Colombo, A. De Rosa, A. Marchese:
Improved stability of optimal traffic paths
Calc. Var. Partial Differential Equations 2017
M. Colombo, L. Spolaor, B. Velichkov:
A logarithmic epiperimetric inequality for the obstacle problem
Geom. Funct. Anal. (Accepted Paper) 2017
M. Colombo, L. Spolaor, B. Velichkov:
Direct epiperimetric inequalities for the thin obstacle problem and applications
Comm. Pure Appl. Math. (Accepted Paper) 2017
M. Colombo, N. Edelen, L. Spolaor:
The singular set of minimal surfaces near polyhedral cones
JDG (Accepted Paper) 2017
M. Colombo, A. De Rosa, A. Marchese:
Stability for the mailing problem
J. Math. Pures Appl. 2018
P. Baroni, M. Colombo, G. Mingione:
Regularity for general functionals with double phase
Calc. Var. Partial Differ. Equ. 2018
M. Colombo, L. Spolaor, B. Velichkov:
On the asymptotic behavior of the solutions to parabolic variational inequalities
J. Reine Agnew. Math. (Accepted Paper) 2018
M. Colombo, C. De Lellis, L. De Rosa :
Ill-posedness of Leray solutions for the ipodissipative Navier--Stokes equations
Comm. Math. Phys. Vol. 362, N. 2, p. 659-688, 2018
M. Colombo, S. Di Marino, F. Stra:
Continuity of multi-marginal optimal transport with repulsive cost
(Submitted Paper) 2019
M. Colombo, M. Fathi:
Bounds on optimal transport maps onto log-concave measures
(Preprint) 2019
M. Colombo, A. De Rosa, A. Marchese:
On the well-posedness of branched transportation
Comm. Pure App. Math. 2019
M. Colombo, A. De Rosa, A. Marchese, P. Pegon, A. Prouff:
Stability of optimal traffic plans in the irrigation problem
(Submitted Paper) 2020
M. Colombo, R. Tione:
On the commutativity of flows of rough vector fields
(Preprint) 2020
M. Colombo, C. De Lellis, A. Massaccesi:
The generalized Caffarelli-Kohn-Nirenberg Theorem for the hyperdissipative Navier-Stokes system
Comm. Pure Appl. Math. Vol. 73, N. 3, p. 609-663, 2020
E. Bruè, M. Colombo, C. De Lellis:
Positive solutions of transport equations and classical nonuniqueness of characteristic curves
Arch. Rat. Mech. Anal. (Accepted Paper) 2020
M. Colombo, G. Crippa, E. Marconi, L. V. Spinolo:
Local limit of nonlocal traffic models: convergence results and total variation blow-up
Ann. de l'institute H. Poincaré, Analyse non linéaire (Accepted Paper) 2021
M. Colombo, L. Spolaor, B. Velichkov:
Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem
Interfaces and Free Boundaries (Accepted Paper) 2021
M. Colombo, S. Di Marino, F. Stra:
First order expansion in the semiclassical limit of the Levy-Lieb
functional
(preprint) 2021