[colombom]

Assistant Professor, EPFL Lausanne

**Email:** *maria.colombo AT epfl.ch*

**Home-page:** https://amcv.epfl.ch

- E. BruĂ¨ - M. Colombo - C. De Lellis (Preprint)

Positive solutions of transport equations and classical nonuniqueness of characteristic curves (2020) - M. Colombo - A. De Rosa - A. Marchese - P. Pegon - A. Prouff (Submitted Paper)

Stability of optimal traffic plans in the irrigation problem (2020) - S. Di Marino - F. Stra - M. Colombo (Submitted Paper)

Continuity of multi-marginal optimal transport with repulsive cost (2019) - M. Colombo - L. Spolaor - B. Velichkov (Preprint)

Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem (2019) - M. Colombo - M. Fathi (Preprint)

Bounds on optimal transport maps onto log-concave measures (2019) - M. Colombo - A. De Rosa - A. Marchese (
*Comm. Pure App. Math.*)

On the well-posedness of branched transportation (2019) - M. Colombo - A. De Rosa - A. Marchese (
*J. Math. Pures Appl.*)

Stability for the mailing problem (2018) - P. Baroni - M. Colombo - G. Mingione (
*Calc. Var. Partial Differ. Equ.*)

Regularity for general functionals with double phase (2018) - M. Colombo - L. Spolaor - B. Velichkov (Accepted Paper:
*J. Reine Agnew. Math.*)

On the asymptotic behavior of the solutions to parabolic variational inequalities (2018) - S. Bianchini - M. Colombo - G. Crippa - L. V. Spinolo (Submitted Paper)

Optimality of integrability estimates for advection-diffusion equations (2017) - M. Colombo - A. Figalli - Y. Jhaveri (Accepted Paper:
*Ann. Sc. Norm. Super. Pisa Cl. Sci.*)

Lipschitz changes of variables between perturbations of log-concave measures (2017) - L. Ambrosio - M. Colombo - A. Figalli (Accepted Paper:
*Duke Math. J.*)

On the Lagrangian structure of transport equations: the Vlasov-Poisson system (2017) - M. Colombo - A. De Rosa - A. Marchese - S. Stuvard (
*Nonlinear Analysis*)

On the lower semicontinuous envelope of functionals defined on polyhedral chains (2017) - M. Colombo - L. Spolaor (Accepted Paper:
*CAG*)

Quantitative estimate on singularities in isoperimetric clusters (2017) - M. Colombo - G. Crippa - L. V. Spinolo (Preprint)

On the singular local limit for conservation laws with nonlocal fluxes (2017) - M. Colombo - L. Spolaor - B. Velichkov (Accepted Paper:
*Geom. Funct. Anal.*)

A logarithmic epiperimetric inequality for the obstacle problem (2017) - M. Colombo - C. De Lellis - L. De Rosa (Accepted Paper:
*To appear in Comm. Math. Phys.*)

Ill-posedness of Leray solutions for the ipodissipative Navier--Stokes equations (2017) - M. Colombo - A. De Rosa - A. Marchese (
*Calc. Var. Partial Differential Equations*)

Improved stability of optimal traffic paths (2017) - M. Colombo - L. Spolaor - B. Velichkov (Accepted Paper:
*Comm. Pure Appl. Math.*)

Direct epiperimetric inequalities for the thin obstacle problem and applications (2017) - M. Colombo - C. De Lellis - A. Massaccesi (Accepted Paper)

The generalized Caffarelli-Kohn-Nirenberg Theorem for the hyperdissipative Navier-Stokes system (2017) - M. Colombo - N. Edelen - L. Spolaor (Accepted Paper:
*JDG*)

The singular set of minimal surfaces near polyhedral cones (2017) - A. Braides - M. Colombo - M. Gobbino - M. Solci (
*C. R. Acad. Sci. Paris, Ser. I*)

Minimizing movements along a sequence of functionals and curves of maximal slope (2016) - M. Colombo - F. Maggi (Accepted Paper:
*Nonlinear Analysis*)

Existence and almost everywhere regularity of isoperimetric clusters for fractional perimeters (2016) - P. Baroni - M. Colombo - G. Mingione (
*St. Petersburg Math. J.*)

Non-autonomous functionals, borderline cases and related function classes (2016) - M. Colombo - G. Crippa - S. Spirito (Accepted Paper:
*Calc. Var. PDE*)

Renormalized solutions to the continuity equation with an integrable damping term (2015) - L. Ambrosio - M. Colombo - A. Figalli (Accepted Paper:
*Arch. Ration. Mech. Anal.*)

Existence and uniqueness of maximal regular flows for non-smooth vector fields (2015) - M. Colombo (Phd Thesis)

Flows of non-smooth vector fields and degenerate elliptic equations (2015) - M. Colombo - F. Stra (Accepted Paper:
*Math. Models Methods Appl. Sci.*)

Counterexamples in multimarginal optimal transport with Coulomb cost and spherically symmetric data (2015) - P. Baroni - M. Colombo - G. Mingione (
*Nonlinear Analysis*)

Harnack inequalities for double phase functionals (2015) - M. Colombo - E. Indrei (Accepted Paper:
*Math. Res. Lett.*)

Obstructions to regularity in the classical Monge problem (2014) - M. Colombo - S. Di Marino (Accepted Paper:
*Ann. Mat. Pura Appl.*)

Equality between Monge and Kantorovich multimarginal problems with Coulomb cost (2013) - M. Colombo - A. Figalli (Accepted Paper:
*Discrete Contin. Dyn. Syst.*)

An excess-decay result for a class of degenerate elliptic equations (2013) - M. Colombo - L. De Pascale - S. Di Marino (Accepted Paper:
*Canad. J. Math.*)

Multimarginal Optimal Transpor Maps for 1-Dimensional Repulsive Costs (2013) - F. Cagnetti - M. Colombo - G. De Philippis - F. Maggi (Accepted Paper:
*Anal. PDE*)

Rigidity of equality cases in Steiner's perimeter inequality (2013) - F. Cagnetti - M. Colombo - G. De Philippis - F. Maggi (Accepted Paper:
*J. Eur. Math. Soc.*)

Essential connectedness and the rigidity problem for Gaussian symmetrization (2013) - E. Bardelli - M. Colombo - A. C. G. Mennucci - A. Yezzi (
*Fifth Workshop on Non-Rigid Shape Analysis and Deformable Image Alignment (NORDIA'12)*)

Multiple Object Tracking via Prediction and Filtering with a Sobolev-type Metric on Curves (2012) - M. Colombo - A. Figalli (Accepted Paper:
*J. Math. Pures Appl.*)

Regularity results for very degenerate elliptic equations (2012) - L. Ambrosio - M. Colombo - G. De Philippis - A. Figalli (Accepted Paper:
*Discrete Contin. Dyn. Syst.*)

A global existence result for the semigeostrophic equations in three dimensional convex domains (2012) - L. Ambrosio - M. Colombo - G. De Philippis - A. Figalli (Accepted Paper:
*Comm. Partial Differential Equations*)

Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case (2012) - L. Ambrosio - M. Colombo - S. Di Marino (Accepted Paper:
*Advanced Studies in Pure Mathematics: "Variational methods for evolving objects"*)

Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope (2012) - M. Colombo - M. Gobbino (Accepted Paper:
*Math. Models Methods Appl. Sci.*)

Passing to the limit in maximal slope curves: from a regularized Perona-Malik equation to the total variation flow (2011) - M. Colombo - M. Gobbino (Accepted Paper:
*SIAM J. Math. Anal.*)

Slow time behavior of the semidiscrete Perona-Malik scheme in dimension one (2010)

*2 jun 2020:*(Webinar) Nonunique characteristic curves of Sobolev vector fields*16 jun 2014:*Equality cases and rigidity in symmetrization inequalities*5 dec 2012:*Regularity results for a very degenerate elliptic equation with applications to traffic dynamic*30 mar 2011:*Slow time behavior of different approximations of the Perona-Malik equation

*1 jul 2019 - 5 jul 2019:*European Mathematical Society Summer School "Partial differential equations from theory to applications"*11 jun 2018 - 15 jun 2018:*Geometric Measure Theory in Verona*25 may 2018 - 25 may 2018:*Brescia-Trento Nonlinear Day Ed. II*3 jul 2017 - 6 jul 2017:*Recent Advances in PDEs and the Calculus of Variations*25 oct 2016 - 28 oct 2016:*Workshop in Geometric Measure Theory, Shape Optimisation and Free Boundaries*16 jun 2014 - 20 jun 2014:*Isoperimetric Problems Between Analysis and Geometry

*24 apr 2017 - 26 apr 2017:*Transport problems in Zurich