See also on ZORA

BOOKS and LECTURE NOTES

C. De Lellis
Il teorema di Schlaefli: un invito alla quarta dimensione
The paper, in italian, has appeared first in the journal "il Volterriano". The file which can be downloaded here contains minor modifications and will be published by Rivista dell'UMI. PDF  

C. De Lellis
Il teorema di Liouville ovvero perche' ``non esiste'' la primitiva di exp(x^2)
The paper, in italian, has appeared first in the journal "il Volterriano". The file which can be downloaded here contains minor modifications and has been published by Rivista dell'UMI. PDF  Volterriano

C. De Lellis
Errata to ``Il teorema di Liouville ovvero perche' ``non esiste'' la primitiva di exp(x^2)''
PDF

C. De Lellis
Allard's interior regularity theorem: an invitation to stationary varifolds
To appear in the Collections of the CMSA Harvard PDF  

C. De Lellis
Rectifiable sets, densities and tangent measures
Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), Zürich. PDF  
EMS Publishing House


C. De Lellis
Errata to ``Lecture Notes on Rectifiable Sets, Densities, and Tangent Measures''
PDF

M. Barsanti, F. Conti, C. De Lellis, T. Franzoni
Le Olimpiadi della Matematica. Seconda Edizione
PDF
Zanichelli


GEOMETRIC MEASURE THEORY

C. De Lellis, A. Marchese, E. Spadaro, D. Valtorta
Rectifiability and upper Minkowski bounds for singularities of harmonic Q-valued maps
PDF

C. De Lellis, J. Ramic
Min-max theory for minimal hypersurfaces with boundary
PDF

C. De Lellis, A. De Rosa, F. Ghiraldin
A direct approach to the anisotropic Plateau's problem
To appear in Advances in Calc. Var. PDF  

C. De Lellis
$2$-dimensional almost area minimizing currents
Boll. Unione Mat. Ital. 9 (2016), no. 1, 3–67. PDF  

C. De Lellis, E. Spadaro, L. Spolaor
Regularity theory for 2-dimensional almost minimal currents III: blowup
PDF

C. De Lellis, E. Spadaro, L. Spolaor
Regularity theory for 2-dimensional almost minimal currents II: branched center manifold
To appear in Annals of PDEs PDF  

C. De Lellis, E. Spadaro, L. Spolaor
Regularity theory for 2-dimensional almost minimal currents I: Lipschitz approximation
To appear in Transactions of the AMS PDF  

C. De Lellis, E. Spadaro, L. Spolaor
Uniqueness of tangent cones for 2-dimensional almost minimizing currents
Comm. Pure Appl. Math. 70, 1402-1421 PDF  

C. De Lellis
The size of the singular set of area-minimizing currents
Surveys in differential geometry 2016. Advances in geometry and mathematical physics, 1–83, Surv. Differ. Geom., 21, Int. Press, Somerville, MA, 2016. PDF  

C. De Lellis
The regularity of minimal surfaces in higher codimension
Current developments in mathematics 2014, 153–229, Int. Press, Somerville, MA, 2016. PDF  

C. De Lellis, F. Ghiraldin, F. Maggi
A direct approach to Plateau's problem
To appear in Journal of the EMS PDF  

C. De Lellis, M. Focardi, B. Ruffini
A note on the Hausdorff dimension of the singular set for minimizers of the Mumford-Shah functional
Adv. Calc. Var. 7, pp. 539-545, 2014 PDF  
ACV


C. De Lellis, E. Spadaro
Regularity of area-minimizing currents III: blow-up
Ann. of Math. (2) 183 (2016), no. 2, 577–617. PDF  

C. De Lellis, E. Spadaro
Regularity of area-minimizing currents II: center manifold
Ann. of Math. (2) 183 (2016), no. 2, 499–575. PDF  

C. De Lellis, E. Spadaro
Regularity of area-minimizing currents I: L^p gradient estimates
Geom. Funct. Anal. 24 (2014), no. 6, 1831–1884. PDF  

C. De Lellis
Errata to "Regularity of area-minimizing currents I: L^p gradient estimates"
PDF

C. De Lellis, E. Spadaro
Multiple valued functions and integral currents
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 14 (2015), no. 4, 1239–1269. PDF  

L. Ambrosio, C. De Lellis, T. Schmidt
Partial regularity for mass-minimizing currents in Hilbert spaces.
To appear in CRELLE PDF  

C. De Lellis, M. Focardi
Density lower bound estimates for local minimizers of the 2d Mumford-Shah energy
Manuscripta Math. 142 (2013), 215-232. PDF  

C. De Lellis, M. Focardi
Higher integrability of the gradient for minimizers of the 2d Mumford-Shah energ
J. Math. Pures Appl. (9) 100 (2013), 391-409. PDF  

C. De Lellis
Hyperbolic equations and SBV functions
Journées équations aux dérivées partielles (2010), Exp. No. 6, 10 p. PDF  
Journées équations aux dérivées partielles


C. De Lellis, E. Spadaro
Center manifold: a case study
To appear in the Proceedings for the 2009 Conference in honor of De Giorgi and Stampacchia, held in Erice
Discrete and Continuous Dynamical Systems Volume 31, Issue 4, Pages : 1249 - 1272, 2011 PDF  
Discrete and Continuous Dynamical Systems


C. De Lellis
Errata to "Center manifold: a case study"
PDF

C. De Lellis, M. Focardi, E. Spadaro
Lower semicontinuous functionals for Almgren's multiple valued functions
Annales Academiae Scientiarum Fennicae vol. 36 pp. 393-410 (2011) PDF  
Annales Academiae Scientiarum Fennicae


C. De Lellis, D. Tasnady
The existence of embedded minimal hypersurfaces
J. Differential Geom. 95 (2013), no. 3, 355–388. PDF  
Journal of Differential Geometry


S. Bianchini, C. De Lellis, R. Robyr
SBV regularity for Hamilton-Jacobi equations in R^n.
Arch. Ration. Mech. Anal. 200 (2011) 1003-1021 PDF  
ARMA


C. De Lellis
Errata to ``SBV regularity for Hamilton-Jacobi equations in R^n''
PDF

C. De Lellis, E. Spadaro
Q-valued functions revisited
Memoirs of the AMS 211 (2011), no. 991. PDF  
Memoirs of the AMS


C. De Lellis
Errata to "Q-valued functions revisited"
PDF

C. De Lellis
Almgren's Q-valued functions revisited
Proceedings of the International Congress of Mathematicians Hyderabad, India, 2010 PDF  

C. De Lellis, F. Pellandini
Genus bounds for minimal surfaces arising from min-max constructions.
J. Reine Angew. Math. 644 (2010), 47–99. PDF  
Crelle


C. De Lellis
A note on Alberti's rank-one theorem.
Transport equations and multi-D hyperbolic conservation laws, 61–74, Lect. Notes Unione Mat. Ital., 5, Springer, Berlin, 2008. PDF  
Springer


C. De Lellis
Errata to ``A note to Alberti's rank-one theorem''
PDF

C. De Lellis, C. R. Grisanti, P. Tilli
Regular selections for multiple-valued functions.
Ann. Mat. Pura Appl. (4) 183 (2004), no. 1, 79–95. PDF  
Ann. Mat. Pura Appl.


T. H. Colding, C. De Lellis
The min-max construction of minimal surfaces.
Surveys in differential geometry, Vol. VIII (Boston, MA, 2002), 75–107, Int. Press, Somerville, MA, 2003. PDF  

C. De Lellis
Some fine properties of currents and applications to distributional Jacobians.
Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), no. 4, 815–842. PDF  
Proc. Roy. Soc. Edinburgh


C. De Lellis
Errata to "Some fine properties of currents and applications to distributional jacobians"
PDF

EULER and NAVIER-STOKES EQUATIONS

M. Colombo, C. De Lellis, L. De Rosa
Ill-posedness of Leray solutions for the ipodissipative Navier--Stokes equations
PDF

T. Buckmaster, C. De Lellis, L. Székelyhidi Jr., V. Vicol
Onsager's conjecture for admissible weak solutions
PDF

C. De Lellis, L. Székelyhidi Jr.
High dimensionality and h-principle in PDE
Bull. Amer. Math. Soc. (N.S.) 54 (2017), no. 2, 247–282. PDF  

C. De Lellis, L. Székelyhidi Jr.
The $h$-principle and Onsager's conjecture
Eur. Math. Soc. Newsl. No. 95 (2015), 19–24. PDF  

T. Buckmaster, C. De Lellis, P. Isett, L. Székelyhidi Jr.
Anomalous dissipation for 1/5-Hoelder Euler flows
Ann. of Math. (2) 182 (2015), no. 1, 127–172. PDF  
Ann. of Math.


C. De Lellis
Errata to "Anomalous dissipation for 1/5-Hoelder Euler flows"
PDF

T. Buckmaster, C. De Lellis, L. Székelyhidi Jr.
Dissipative Euler flows with Onsager-critical spatial regularity
Comm. Pure Appl. Math. 69 (2016), no. 9, 1613–1670. PDF  

T. Buckmaster, C. De Lellis, L. Székelyhidi Jr.
Transporting microstructure and dissipative Euler flows
PDF

C. De Lellis, L. Székelyhidi Jr.
Dissipative Euler Flows and Onsager's Conjecture
J. Eur. Math. Soc. (JEMS) 16 (2014), no. 7, 1467–1505. PDF  

C. De Lellis
Errata to "Dissipative Euler flows and Onsager's conjecture"
PDF

A. Choffrut, C. De Lellis, L. Székelyhidi Jr.
Dissipative continuous Euler flows in two and three dimensions
PDF

C. De Lellis, L. Székelyhidi Jr.
Continuous dissipative Euler flows and a conjecture of Onsager.
European Congress of Mathematics, 13–29, Eur. Math. Soc., Zürich, 2013. PDF  

C. De Lellis
Errata to ``Continuous dissipative Euler flows and a conjecture of Onsager''
PDF

C. De Lellis, L. Székelyhidi Jr.
Dissipative continuous Euler flows
Inventiones Mathematicae 193, Issue 2 (2013), Page 377-407 PDF  
Inventiones


C. De Lellis, L. Székelyhidi Jr.
The h-principle and the equations of fluid dynamics.
Bull. Amer. Math. Soc. 49, 347-375, 2012 PDF  
Bull. AMS


C. De Lellis
Errata to "The h-principle and the equations of fluid dynamics"
PDF

Y. Brenier, C. De Lellis, L. Székelyhidi Jr.
Weak-strong uniqueness for measure-valued Solutions
Comm. Math. Phys. 305 (2011), 351-361 PDF  
Comm. Math. Phys.


C. De Lellis, L. Székelyhidi Jr.
On admissibility criteria for weak solutions of the Euler equations.
Arch. Ration. Mech. Anal. 195 (2010), no. 1, 225–260. PDF  
Arch. Ration. Mech. Anal.


C. De Lellis
Errata to "On admissibility criteria for weak solutions of the Euler equations"
PDF

C. De Lellis
Le equazioni di Eulero dal punto di vista delle inclusioni differenziali (Italian)
Boll. Unione Mat. Ital. (9) 1 (2008), no. 3, 873–879 PDF  
Boll. UMI


C. De Lellis, L. Székelyhidi Jr.
The Euler equations as a differential inclusion.
Ann. of Math. (2) 170 (2009), no. 3, 1417–1436. PDF  
Ann. of Math.


DIFFERENTIAL GEOMETRY

A. Carlotto, C. De Lellis
Min-max embedded geodesic lines on asymptotically conical surfaces
PDF

C. De Lellis, D. Inauen, L. Székelyhidi Jr.
A Nash-Kuiper theorem for $C^{1,\sfrac{1}{5}-\delta}$ immersions of surfaces in $3$ dimensions
To appear in Revista matemática Iberoamericana PDF  

C. De Lellis, P. M. Topping
Almost Schur Lemma
Calc. Var. 43 (2012) 347-354 PDF  
Calc. Var.


S. Conti, C. De Lellis, L. Székelyhidi Jr.
h-principle and rigidity for C^{1,\alpha} isometric embeddings
Nonlinear Partial Differential Equations
Abel Symposia Volume 7, 2012, pp 83-116 PDF  
Proceedings of the Abel Symposium 2010


T. H. Colding, C. De Lellis, W. P. Minicozzi II
Three circles theorems for Schrödinger operators on cylindrical ends and geometric applications.
Comm. Pure Appl. Math. 61 (2008), no. 11, 1540–1602. PDF  
CPAM


C. De Lellis, S. Müller
A $C^0$ estimate for nearly umbilical surfaces.
Calc. Var. Partial Differential Equations 26 (2006), no. 3, 283–296. PDF  
Calc. Var.


C. De Lellis, S. Müller
Optimal rigidity estimates for nearly umbilical surfaces.
J. Differential Geom. 69 (2005), no. 1, 75–110. PDF  
JDG


T. H. Colding, C. De Lellis
Singular limit laminations, Morse index, and positive scalar curvature.
Topology 44 (2005), no. 1, 25–45. PDF  
Topology


TRANSPORT EQUATIONS

C. De Lellis, P. Gwiazda, A. Swierczewska-Gwiazda
Transport equation with integral terms
Calc. Var. Partial Differential Equations 55 (2016), no. 5, Paper No. 128, 17 pp. PDF  

C. De Lellis
ODEs with Sobolev coefficients: the Eulerian and the Lagrangian approach.
Discrete Contin. Dyn. Syst. Ser. S 1 (2008), no. 3, 405–426. PDF  
DCDS


C. De Lellis
Ordinary differential equations with rough coefficients and the renormalization theorem of Ambrosio [after Ambrosio, DiPerna, Lions].
Séminaire Bourbaki. Vol. 2006/2007. Astérisque No. 317 (2008), Exp. No. 972, viii, 175–203. PDF  
Séminaire Bourbaki.


G. Crippa, C. De Lellis
Estimates and regularity results for the DiPerna-Lions flow.
J. Reine Angew. Math. 616 (2008), 15–46. PDF  
Crelle


C. De Lellis
Notes on hyperbolic systems of conservation laws and transport equations.
Handbook of differential equations: evolutionary equations. Vol. III, 277–382, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2007.
WARNING. THIS PDF IS NOT THE MOST UPDATED VERSION: PDF  
Handbook of EDE


C. De Lellis
Errata to "Notes on hyperbolic systems of conservation laws and transport equations."
PDF

L. Ambrosio, C. De Lellis, J. Maly
On the chain rule for the divergence of BV-like vector fields: applications, partial results, open problems.
Perspectives in nonlinear partial differential equations, 31–67, Contemp. Math., 446, Amer. Math. Soc., Providence, RI, 2007. PDF  

C. De Lellis
The chain rule for the divergence of BV-like vector fields.
Hyperbolic problems: theory, numerics and applications. I, 105–112, Yokohama Publ., Yokohama, 2006 PDF  

G. Crippa, C. De Lellis
Oscillatory solutions to transport equations.
Indiana Univ. Math. J. 55 (2006), no. 1, 1–13. PDF  
Indiana Univ. Math. J.


HYPERBOLIC CONSERVATION LAWS

C. De Lellis, Radu Ignat
A regularizing property of the 2d-eikonal equation
Comm. Partial Differential Equations 40 (2015), no. 8, 1543–1557. PDF  

E. Chiodaroli, C. De Lellis, O. Kreml
Surprising solutions to the isentropic Euler system of gas dynamics
Hyperbolic problems: theory, numerics, applications, 1–10, AIMS Ser. Appl. Math., 8, Am. Inst. Math. Sci. (AIMS), Springfield, MO, 2014. PDF  

E. Chiodaroli, C. De Lellis, O. Kreml
Global ill-posedness of the isentropic system of gas dynamics
Comm. Pure Appl. Math. 68 (2015), no. 7, 1157–1190. PDF  

C. De Lellis
Ill-posedness for bounded admissible solutions of the 2-dimensional p--system.
Hyperbolic problems: theory, numerics and applications, 269–278, Proc. Sympos. Appl. Math., 67, Part 1, Amer. Math. Soc., Providence, RI, 2009. PDF  

C. De Lellis, F. Golse
A quantitative compactness estimate for scalar conservation laws.
Comm. Pure Appl. Math. 58 (2005), no. 7, 989–998. PDF  
CPAM


C. De Lellis
Blowup of the BV norm in the multidimensional Keyfitz and Kranzer system.
Duke Math. J. 127 (2005), no. 2, 313–339. PDF  
Duke Math. J.


L. Ambrosio, F. Bouchut, C. De Lellis
Well-posedness for a class of hyperbolic systems of conservation laws in several space dimensions.
Comm. Partial Differential Equations 29 (2004), no. 9-10, 1635–1651. PDF  
Comm. PDE


C. De Lellis
Errata to "Well-posedness for the for a class of hyperbolic systems of conservation laws in several space dimensions."
PDF

L. Ambrosio, C. De Lellis
A note on admissible solutions of 1D scalar conservation laws and 2D Hamilton-Jacobi equations.
J. Hyperbolic Differ. Equ. 1 (2004), no. 4, 813–826. PDF  
JHDE


C. De Lellis, F. Otto, M. Westdickenberg
Minimal entropy conditions for Burgers equation.
Quart. Appl. Math. 62 (2004), no. 4, 687–700. PDF  
Quart. Appl. Math.


C. De Lellis, T. Rivière
The rectifiability of entropy measures in one space dimension.
J. Math. Pures Appl. (9) 82 (2003), no. 10, 1343–1367. PDF  
J. Math. Pures Appl.


C. De Lellis
Errata to "The rectifiability of entropy measures in one space dimension".
PDF

C. De Lellis, F. Otto, M. Westdickenberg
Structure of entropy solutions for multi-dimensional scalar conservation laws.
Arch. Ration. Mech. Anal. 170 (2003), no. 2, 137–184 PDF  
ARMA


C. De Lellis, M. Westdickenberg
On the optimality of velocity averaging lemmas.
Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003), no. 6, 1075–1085. PDF  
Ann. IHP


L. Ambrosio, C. De Lellis
Existence of solutions for a class of hyperbolic systems of conservation laws in several space dimensions.
Int. Math. Res. Not. 2003, no. 41, 2205–2220. PDF  
IMRN


CALCULUS OF VARIATIONS

C. De Lellis, F. Ghiraldin
An extension of the identity Det=det.
C. R. Math. Acad. Sci. Paris 348 (2010), no. 17-18, 973–976 PDF  
C. R. Math. Acad. Sci. Paris


S. Conti, C. De Lellis
Sharp upper bounds for a variational problem with singular perturbation.
Math. Ann. 338 (2007), no. 1, 119–146. PDF  
Math. Ann.


C. De Lellis, L. Székelyhidi Jr.
Simple proof of two-well rigidity.
C. R. Math. Acad. Sci. Paris 343 (2006), no. 5, 367–370 PDF  
C. R. Math. Acad. Sci. Paris


S. Conti, C. De Lellis
Some remarks on the theory of elasticity for compressible Neohookean materials.
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 2 (2003), no. 3, 521–549. PDF  
Annali SNS


C. De Lellis
Errata to "Some remarks on the theory of elasticity for compressible Neohookean materials"
PDF

S. Conti, C. De Lellis, S. Müller, M. Romeo
Polyconvexity equals rank-one convexity for connected isotropic sets in $\Bbb M^{2\times 2}$.
C. R. Math. Acad. Sci. Paris 337 (2003), no. 4, 233–238. PDF  
C. R. Math. Acad. Sci. Paris


C. De Lellis, F. Otto
Structure of entropy solutions to the eikonal equation.
J. Eur. Math. Soc. (JEMS) 5 (2003), no. 2, 107–145. PDF  
JEMS


C. De Lellis
Some remarks on the distributional Jacobian.
Nonlinear Anal. 53 (2003), no. 7-8, 1101–1114. PDF  
Nonlinear Anal.


C. De Lellis
An example in the gradient theory of phase transitions.
ESAIM Control Optim. Calc. Var. 7 (2002), 285–289 PDF  
ESAIM COCV


L. Ambrosio, C. De Lellis, C. Mantegazza
Line energies for gradient vector fields in the plane
Calc. Var. Partial Differential Equations 9 (1999), no. 4, 327–255. PDF  
Calc. Var.


OTHER

C. De Lellis, D. Inauen
Fractional Sobolev regularity for the Brouwer degree
To appear in Comm. in PDEs PDF  

C. De Lellis, L. Székelyhidi Jr.
John Nash's nonlinear iteration
Forthcoming in Memorial Volume for Professor John Nash, eds. Joseph Kohn and Hong Jun, World Scientific Publishers, 2017 PDF  

C. De Lellis
The masterpieces of John Forbes Nash Jr.
To appear in H. Holden and R. Piene (editors): The Abel Prize 2013–2017. Springer Verlag. PDF  

C. De Lellis, R. Robyr
Hamilton-Jacobi equations with obstacles
Arch. Ration. Mech. Anal. 200 (2011) 1051-1073 PDF  
ARMA


A. Bressan, C. De Lellis
Existence of optimal strategies for a fire confinement problem.
Comm. Pure Appl. Math. 62 (2009), no. 6, 789–830. PDF  
CPAM


C. De Lellis, T. Kappeler, P. Topalov
Low-regularity solutions of the periodic Camassa-Holm equation.
Comm. Partial Differential Equations 32 (2007), no. 1-3, 87–126. PDF  
Comm. PDE


C. De Lellis, G. Royer-Carfagni
Interaction of fractures in tensile bars with non-local spatial dependence.
J. Elasticity 65 (2001), no. 1-3, 1–31 (2002). PDF  
J of E