cvgmt: Camillo De Lellis

Calculus of Variations and Geometric Measure Theory

Camillo De Lellis

[delellis]

Full Professor, Institute for Advanced Study, Princeton

Email: camillo.delellis AT ias.edu

Home-page: https://www.math.ias.edu/delellis/

arxiv id: delellis_c_1

Available papers (132):

C. De Lellis - P. Minter - A. Skorobogatova (Preprint)
Fine Structure of Singularities in Area-Minimizing Currents Mod$(q)$ (2024)
C. De Lellis - S. Nardulli - S. Steinbrüchel (Publications Mathématiques de l' I.H.É.S.)
An Allard-type boundary regularity theorem for $2d$ minimizing currents at smooth curves with arbitrary multiplicity (2024)
C. De Lellis - F. Glaudo - A. Massaccesi - D. Vittone (Preprint)
Besicovitch's $\frac{1}{2}$ problem and linear programming (2024)
C. De Lellis (Preprint)
Caffarelli's work on elliptic free boundary problems (2024)
C. De Lellis - J. Hirsch - A. Marchese - L. Spolaor - S. Stuvard (Nonlinear Anal.)
Excess decay for minimizing hypercurrents mod $2Q$ (2024)
A. Bressan - C. De Lellis (Preprint)
A Remark on the Uniqueness of Solutions to Hyperbolic Conservation Laws (2023)
C. De Lellis - A. Skorobogatova (Preprint)
The fine structure of the singular set of area-minimizing integral currents I: the singularity degree of flat singular points (2023)
C. De Lellis - M. Focardi (Lecture Notes)
The regularity theory for the Mumford-Shah functional on the plane (2023)
C. De Lellis - S. Nardulli - S. Steinbrüchel (Nonlinear Analysis)
Uniqueness of boundary tangent cones for $2$-dimensional area-minimizing currents (2023)
C. De Lellis - A. Skorobogatova (Preprint)
The fine structure of the singular set of area-minimizing integral currents II: rectifiability of flat singular points with singularity degree larger than $1$ (2023)
C. De Lellis - P. Minter - A. Skorobogatova (Preprint)
The fine structure of the singular set of area-minimizing integral currents III: Frequency 1 flat singular points and $\mathcal{H}^{m-2}$-a.e. uniqueness of tangent cones (2023)
C. De Lellis - I. Fleschler (Accepted Paper: Mathematical Research Letters)
An elementary rectifiability lemma and some applications (2023)
C. De Lellis - J. Hirsch - A. Marchese - S. Stuvard (Comm. Pure Appl. Math.)
Area minimizing currents mod $2Q$: linear regularity theory (2022)
E. Bruè - M. Colombo - G. Crippa - C. De Lellis - M. Sorella (Communications on Pure and Applied Analysis)
Onsager critical solutions of the forced Navier-Stokes equations (2022)
E. Bruè - C. De Lellis (Comm. Math. Phys.)
Anomalous dissipation for the forced 3D Navier-Stokes equations (2022)
C. De Lellis - J. Hirsch - A. Marchese - L. Spolaor - S. Stuvard (Submitted Paper)
Fine structure of the singular set of area minimizing hypersurfaces modulo $p$ (2022)
C. De Lellis - L. J. Székelyhidi (Accepted Paper: Philosophical Transactions of the Royal Society A)
Weak stablity and closure in turbulence (2021)
C. De Lellis (Preprint)
An Allard-type boundary regularity theorem for 2d minimizing currents at smooth curves with arbitrary multiplicity (2021)
C. De Lellis (Proceedings)
The regularity theory for the area functional (in geometric measure theory) (2021)
C. De Lellis - J. Hirsch - A. Marchese - L. Spolaor - S. Stuvard (Submitted Paper)
Area minimizing hypersurfaces modulo $p$: a geometric free-boundary problem (2021)
D. Albritton - E. Bruè - M. Colombo - C. De Lellis - V. Giri - M. Janisch - H. Kwon (Accepted Paper: Annals of Mathematics Studies)
Instability and nonuniqueness for the 2d Euler equations in vorticity form, after M. Vishik (2021)
M. Colombo - C. De Lellis - A. Massaccesi (Comm. Pure Appl. Math.)
The generalized Caffarelli-Kohn-Nirenberg Theorem for the hyperdissipative Navier-Stokes system (2020)
C. De Lellis - D. Inauen (Adv. Math.)
$C^{1,\alpha} isometric embeddings of polar caps (2020)
C. De Lellis - E. Spadaro - L. Spolaor (J. Differential Geom.)
Regularity theory for $2$-dimensional almost minimal currents III: blowup (2020)
C. De Lellis - M. P. Reza (Preprint)
The geometry of flat $C^{1,\alpha}$ isometric immersions (2020)
C. De Lellis - J. Hirsch - A. Marchese - S. Stuvard (Geom. Funct. Anal.)
Regularity of area minimizing currents mod $p$ (2020)
C. De Lellis - V. Giri (Accepted Paper: To appear in Annales Mathe'matiques du Que'bec)
Smoothing does not give a selection principle for transport equations with bounded autonomous fields (2020)
C. De Lellis (ICCM Not.)
The Nash-Kuiper Theorem and the Onsager conjecture (2020)
C. De Lellis - H. Kwon (Accepted Paper: To appear in Analysis and PDEs)
On Non-uniqueness of Hoelder continuous globally dissipative Euler flows (2020)
E. Bruè - M. Colombo - C. De Lellis (Arch. Rat. Mech. Anal.)
Positive solutions of transport equations and classical nonuniqueness of characteristic curves (2020)
C. De Lellis - M. Focardi - S. Ghinassi (J. Math. Pures Appl.)
Endpoint regularity for 2d Mumford-Shah minimizers: On a theorem of Andersson and Mikayelyan (2020)
C. De Lellis - Z. Zhao (Preprint)
Dirichlet energy-minimizers with analytic boundary (2019)
A. Carlotto - C. De Lellis (J. Differential Geom.)
Min-max embedded geodesic lines on asymptotically conical surfaces (2019)
T. Buckmaster - C. De Lellis - L. J. Székelyhidi - V. Vicol (Comm. Pure Appl. Math.)
Onsager's conjecture for admissible weak solutions (2019)
C. De Lellis - G. De Philippis - J. Hirsch (Accepted Paper: J. Differential Geom.)
Nonclassical minimizing surfaces with smooth boundary (2019)
C. De Lellis - L. J. Székelyhidi (Notices Amer. Math. Soc.)
On turbulence and geometry: from Nash to Onsager (2019)
C. De Lellis - G. De Philippis - B. Kirchheim - R. Tione (Annales de la Faculte' des Sciences de Toulouse)
Geometric measure theory and differential inclusions (2019)
L. Ambrosio - C. De Lellis - T. Schmidt (J. Reine Angew. Math.)
Partial regularity for mass-minimizing currents in Hilbert spaces (2018)
C. De Lellis - E. Spadaro - L. Spolaor (Transactions AMS)
Regularity theory for $2$-dimensional almost minimal currents I: Lipschitz approximation (2018)
C. De Lellis (Lecture Notes)
Almgren's center manifold in a simple setting (2018)
C. De Lellis (Surveys in Differential Geometry 2017.)
The Onsager Theorem (2018)
C. De Lellis (Proceedings of CMSA Harvard. Nonlinear analysis in geometry and applied mathematics. Part 2)
Allard's interior regularity theorem: an invitation to stationary varifolds (2018)
M. Colombo - C. De Lellis - L. De Rosa (Comm. Math. Phys.)
Ill-posedness of Leray solutions for the ipodissipative Navier--Stokes equations (2018)
C. De Lellis - D. Inauen - L. J. Székelyhidi (Revista matemática Iberoamericana)
A Nash-Kuiper theorem for $C^{1,\frac{1}{5}-\delta}$ immersions of surfaces in $3$ dimensions (2018)
C. De Lellis - A. Marchese - E. Spadaro - D. Valtorta (Comm. Math. Helv.)
Rectifiability and upper Minkowski bounds for singularities of harmonic $Q$-valued maps (2018)
C. De Lellis - G. De Philippis - J. Hirsch - A. Massaccesi (Accepted Paper: To apper in Memoirs of the American Mathematical Society)
On the boundary behavior of mass-minimizing integral currents (2018)
C. De Lellis - A. De Rosa - F. Ghiraldin (Adv. Calc. Var.)
A direct approach to the anisotropic Plateau's problem (2018)
C. De Lellis - L. J. Székelyhidi (Bull. Amer. Math. Soc. (N.S.))
High dimensionality and h-principle in PDE (2017)
C. De Lellis - L. J. Székelyhidi (Accepted Paper)
John Nash's nonlinear iteration (2017)
C. De Lellis - F. Ghiraldin - F. Maggi (JEMS)
A direct approach to Plateau's problem (2017)
C. De Lellis - E. Spadaro - L. Spolaor (Ann. PDE)
Regularity theory for $2$-dimensional almost minimal currents II: branched center manifold (2017)
C. De Lellis - E. Spadaro - L. Spolaor (Comm. Pure Appl. Math.)
Uniqueness of tangent cones for $2$-dimensional almost minimizing currents (2017)
C. De Lellis - D. Inauen (Comm. Partial Differential Equations)
Fractional Sobolev regularity for the Brouwer degree (2017)
C. De Lellis - G. De Philippis - J. Hirsch - A. Massaccesi (Matrix Annals)
Boundary regularity of mass-minimizing integral currents and a question of Almgren (2017)
C. De Lellis - E. Spadaro (Ann. of Math. (2) )
Regularity of area-minimizing currents II: center manifold (2016)
C. De Lellis - E. Spadaro (Ann. of Math. (2))
Regularity of area-minimizing currents III: blow up (2016)
C. De Lellis (Boll. Unione Mat. Ital.)
$2$-dimensional almost area minimizing currents (2016)
C. De Lellis (Accepted Paper: Rivista dell'UMI)
Il teorema di Schlaefli: un invito alla quarta dimensione (2016)
C. De Lellis - P. Gwiazda - S. G. Agnieszka (Calc. Var. Partial Differential Equations)
Transport equation with integral terms (2016)
T. Buckmaster - C. De Lellis - L. J. Székelyhidi (Comm. Pure Appl. Math.)
Dissipative Euler flows with Onsager-critical spatial regularity (2016)
C. De Lellis - J. Ramic (Accepted Paper: To appear in Annales de l'Institut Fourier)
Min-max theory for minimal hypersurfaces with boundary (2016)
C. De Lellis (Surveys in differential geometry)
The size of the singular set of area-minimizing currents (2016)
C. De Lellis (H. Holden and R. Piene (editors): The Abel Prize 2013–2017. Springer Verlag.)
The masterpieces of John Forbes Nash Jr (2016)
C. De Lellis - R. Ignat (Comm. Partial Differential Equations)
A regularizing property of the 2d-eikonal equation (2015)
C. De Lellis - L. J. Székelyhidi (Eur. Math. Soc. Newsl.)
The $h$-principle and Onsager's conjecture (2015)
E. Chiodaroli - C. De Lellis - O. Kreml (Comm. Pure App. Math.)
Global ill-posedness of the isentropic system of gas dynamics (2015)
T. Buckmaster - C. De Lellis - P. Isett - L. J. Székelyhidi (Ann. of Math. (2))
Anomalous dissipation for $1/5$-Hölder Euler flows (2015)
C. De Lellis - E. Spadaro (Ann. Sc. Norm. Super. Pisa Cl. Sci. (5))
Multiple valued functions and integral currents (2015)
C. De Lellis - L. J. László Jr Székelyhidi (J. Eur. Math. Soc. (JEMS))
Dissipative Euler flows and Onsager's conjecture (2014)
C. De Lellis - M. Focardi - B. Ruffini (Adv. Calc. Var.)
A note on the Hausdorff dimension of the singular set for minimizers of the Mumford-Shah energy (2014)
E. Chiodaroli - C. De Lellis - O. Kreml (Proceedings of HYP2012)
Surprising solutions to the isentropic system of gas dynamics (2014)
C. De Lellis - E. Spadaro (Geom. Funct. Anal.)
Regularity of area-minimizing currents I: $L^p$ gradient estimates (2014)
C. De Lellis (Mat. Soc. Cult. Riv. Unione Mat. Ital. (I))
Il teorema di Liouville ovvero perche' "non esiste" la primitiva di $\exp(x^2)$ (2014)
C. De Lellis - M. Focardi (J. Math. Pures Appl.)
Higher integrability of the gradient for minimizers of the 2d Mumford-Shah energy (2013)
C. De Lellis - M. Focardi (Manuscripta Math.)
Density lower bound estimates for local minimizers of the 2d Mumford-Shah energy (2013)
C. De Lellis - L. J. László Jr Székelyhidi (Invent. Math.)
Dissipative continuous Euler flows (2013)
T. Buckmaster - C. De Lellis - L. J. László Jr Székelyhidi (Preprint)
Transporting microstructure and dissipative Euler flows (2013)
C. De Lellis - L. J. László Jr Székelyhidi (European Congress of Mathematics)
Continuous dissipative Euler flows and a conjecture of Onsager (2013)
C. De Lellis - D. Tasnady (Jour. Diff. Geom.)
The existence of embedded minimal hypersurfaces (2013)
A. Choffrut - C. De Lellis - L. J. László Jr Székelyhidi (Preprint)
Dissipative continuous Euler flows in two and three dimensions (2012)
C. De Lellis - L. J. László Jr Székelyhidi (Bull. Amer. Math. Soc. )
The $h$-principle and the equations of fluid dynamics (2012)
S. Conti - C. De Lellis - L. J. Székelyhidi (Nonlinear Partial Differential Equations. Abel Symposia 7.)
h-Principle and Rigidity for $C^{1,\alpha}$ Isometric Embeddings (2012)
C. De Lellis - Peter M. Topping (Calc. Var.)
Almost-Schur lemma (2012)
C. De Lellis - M. Focardi - E. Spadaro (Annales Academiae Scientiarum Fennicae Mathematica)
Lower semicontinuous functionals for Almgren's multiple valued functions (2011)
Y. Brenier - C. De Lellis - L. J. Székelyhidi (Comm. Math. Phys.)
Weak-strong uniqueness for measure-valued Solutions (2011)
C. De Lellis - R. Robyr (Arch. Ration. Mech. Anal.)
Hamilton-Jacobi equations with obstacles (2011)
S. Bianchini - C. De Lellis - R. Robyr (Arch. Ration. Mech. Anal.)
SBV regularity for Hamilton-Jacobi equations in R^n (2011)
C. De Lellis - E. Spadaro (]: Discrete Contin. Dyn. Syst.)
Center manifold: a case study (2011)
C. De Lellis - Emanuele Nunzio Spadaro (Memoirs of the American Mathematical Society)
Q-valued functions revisited (2011)
C. De Lellis - L. J. Székelyhidi (Arch. Ration. Mech. Anal.)
On admissibility criteria for weak solutions of the Euler equations (2010)
C. De Lellis - F. Ghiraldin (C. R. Math. Acad. Sci. Paris)
An extension of Müller's identity $\mathbf{Det} = \mathbf{det}$ (2010)
C. De Lellis (Proceedings of the International Congress of Mathematicians. )
Almgren's $Q$-valued functions revisited (2010)
C. De Lellis - F. Pellandini (J. Reine Angew. Math.)
Genus bounds for minimal surfaces arising from min-max constructions (2010)
C. De Lellis - L. J. Székelyhidi (Ann. of Math.)
The Euler equation as a differential inclusion (2009)
A. Bressan - C. De Lellis (Comm. Pure Appl. Math.)
Existence of optimal strategies for a fire confinement problem (2009)
C. De Lellis (Hyperbolic problems: theory, numerics and applications.)
Ill-posedness for bounded admissible solutions of the $2$-dimensional $p$-system (2009)
T. Colding - C. De Lellis - W. P. I. I. Minicozzi (Comm. Pure App. Math.)
Three circles theorems for Schrödinger operators on cylindrical ends and geometric applications (2008)
G. Crippa - C. De Lellis (J. Reine Angew. Math.)
Estimates and regularity results for the DiPerna--Lions flow (2008)
C. De Lellis (Lecture notes: Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), Zürich.)
Lecture notes on rectifiable sets, densities, and tangent measures (2008)
C. De Lellis (Transport equations and multi-D hyperbolic conservation laws, 61-74, Lect. Notes Unione Mat. Ital., 5, Springer, Berlin..)
A note on Alberti's Rank--one Theorem (2008)
G. Crippa - C. De Lellis (Hyperbolic Problems: Theory, Numerics, Applications)
Regularity and compactness for the DiPerna--Lions flow (2008)
C. De Lellis (Séminaire Bourbaki. Vol. 2006/2007. Astérisque No. 317 )
Ordinary differential equations with rough coefficients and the renormalization theorem of Ambrosio (d'après Ambrosio, DiPerna, Lions) (2007)
S. Conti - C. De Lellis (Math. Ann.)
Sharp upper bounds for a variational problem with singular perturbation (2007)
C. De Lellis - T. Kappeler - P. Topalov (Comm. Partial Differential Equations)
Low--regularity solutions of the Camass--Holm equation (2007)
L. Ambrosio - C. De Lellis - J. Malý (Perspective in nonlinear partial differential equations)
On the chain rule for the divergence of BV like vector fields: applications, partial results, open problems (2007)
C. De Lellis - L. J. Székelyhidi (C. R. Math. Acad. Sci. Paris)
Simple proof of two-well rigidity (2006)
C. De Lellis (Handbook of Differential Equations: Evolutionary Differential Equations)
Notes on hyperbolic systems of conservation laws and transport equations (2006)
G. Crippa - C. De Lellis (Indiana Univ. Math. J.)
Oscillatory solutions to transport equations (2006)
C. De Lellis - S. Müller (Calc. Var. Partial Differential Equations)
A $C^0$--estimate for nearly umbilical surfaces. (2006)
L. Ambrosio - F. Bouchut - C. De Lellis (Comm. Partial Differential Equations)
Well--posedness for a class of hyperbolic systems of conservation laws in several space dimensions (2004)
C. De Lellis (Duke Math. J.)
Blow--up of the BV norm in the multidimensional Keyfitz and Kranzer system (2004)
C. De Lellis - F. Otto - M. Westdickenberg (Quarterly of Applied Mathematics)
Minimal entropy conditions for Burgers equation (2004)
C. De Lellis - F. Golse (Comm. Pure Appl. Math.)
A quantitative compactness estimate for scalar conservation laws (2004)
L. Ambrosio - C. De Lellis (J. Hyperbolic Diff. Equ.)
A note on admissible solutions of 1d scalar conservation laws and 2d Hamilton-Jacobi equations (2004)
C. De Lellis - F. Otto - M. Westdickenberg (Archive for Rational Mechanics and Analysis)
Structure of entropy solutions for multi--dimensional conservation laws (2003)
L. Ambrosio - C. De Lellis (International Mathematics Research Notices)
Existence of solutions for a class of hyperbolic systems of conservation laws in several space dimensions (2003)
C. De Lellis (Nonlinear Analysis: Theory, Methods and Applications)
Some remarks on the distributional Jacobian (2003)
C. De Lellis - F. Otto (J. Eur. Math. Soc.)
Structure of entropy solutions to the eikonal equation (2003)
C. De Lellis - T. Rivière (Journal de Mathématiques Pures et Appliquées)
Concentration estimates for entropy measures (2003)
C. De Lellis - S. Müller (Journal of Differential Geometry)
Sharp rigidity estimates for nearly umbilical surfaces (2003)
S. Conti - C. De Lellis - S. Mueller - M. Romeo (C. R. Math. Acad. Sci. Paris)
Polyconvexity equals rank-one convexity for connected isotropic sets in $M^{2\times 2}$ (2003)
Tobias H. Colding - C. De Lellis (Surveys in differential geometry)
The min--max construction of minimal surfaces (2003)
Tobias H. Colding - C. De Lellis (Topology)
Singular limit laminations, Morse index, and positive scalar curvature (2003)
C. De Lellis - M. Westdickenberg (Ann. Inst. Henry Poincaré Analise Non linéaire)
On the Optimality of Velocity Averaging Lemmas (2002)
C. De Lellis (Ph.D. Thesis)
On the Jacobian of weakly differentiable maps (2002)
C. De Lellis (Control, Optimisation and Calculus of Variations)
An example in the gradient theory of phase transitions (2002)
C. De Lellis - G. Royer Carfagni (Journal of Elasticity)
Interaction of fractures in tensile bars with non local spatial displacement (2001)
S. Conti - C. De Lellis (Ann. Scuola Norm. Sup. Cl. Sci. (5))
Some remarks on the theory of elasticity for compressible Neohookean materials (2001)
C. De Lellis - C. R. Grisanti - P. Tilli (Annali di Matematica Pura ed Applicata)
Regular selection for multiple valued functions (2000)
C. De Lellis (Proc. Roy. Soc. of Ed. A)
Some fine properties of currents and applications to distributional jacobians (2000)
C. De Lellis (Degree Thesis)
Energie di Linea per Campi di Gradienti (1999)
L. Ambrosio - C. De Lellis - C. Mantegazza (Calc. Var.)
Line Energies for Gradient Vector Fields in the Plane (1999)

Seminars:

8 apr 2020: Flows of vector fields: classical and modern
22 jun 2015: Center manifolds and regularity of area-minimizing currents
19 feb 2009: Ipersuperfici minime in varietà Riemanniane
9 jan 2008: Le equazioni di Eulero dal punto di vista delle inclusioni differenziali
6 dec 2001: Some remarks on the theory of elasticity for compressible eohookean materials

Speaker:

16 sep 2024 - 20 sep 2024: Frontiers of the Calculus of Variations: a Celebration of the Mathematics of Gianni Dal Maso
17 jun 2024 - 21 jun 2024: Geometric Measure Theory and applications 2024
24 jul 2023 - 28 jul 2023: Thematic Session on GMT
5 jun 2023 - 9 jun 2023: Vito Volterra Meeting 2023 in Calculus of Variations
1 jul 2019 - 5 jul 2019: Geometric Analysis on Riemannian and Singular Metric Measure spaces (3rd edition)
14 jan 2019 - 17 jan 2019: Alessio Figalli, Fields medallist 2018
6 jul 2018 - 8 jul 2018: Minimal Surfaces and Mean Curvature Flow - A Conference in Honor of Brian White
11 jun 2018 - 15 jun 2018: Geometric Measure Theory in Verona
19 sep 2016 - 23 sep 2016: A Mathematical Tribute to Ennio De Giorgi
15 jul 2013 - 2 aug 2013: School and Workshop on "Geometric Measure Theory and Optimal Transport"
4 sep 2012 - 7 sep 2012: Meeting on Applied Mathematics and Calculus of Variations
2 sep 2012 - 7 sep 2012: ESF-EMS-ERCOM Research Conference on Applied Partial Differential Equations in Physics, Biology and Social Sciences: Classical and Modern Perspectives
1 jun 2012 - 31 jul 2012: Geometric and Analytic techniques in Calculus of Variations and Partial Differential Equations
13 feb 2009 - 13 feb 2009: Le equazioni di Eulero e l'h-principio
12 sep 2005 - 16 sep 2005: Second Summer School `Analysis and Applied Mathematics' in Rome

Organizer:

24 aug 2020 - 4 sep 2020: 2020 Focus Period for the FRG: New Challenges in Geometric Measure Theory
23 jun 2014 - 18 jul 2014: Summer School on Geometric Measure Theory and Geometric Analysis
7 oct 2013 - 11 oct 2013: ERC-Workshop on Geometric Measure Theory, Analysis in Metric Spaces and Real Analysis
30 sep 2013 - 4 oct 2013: ERC-School on Geometric Measure Theory and Real Analysis
15 jul 2013 - 2 aug 2013: School and Workshop on "Geometric Measure Theory and Optimal Transport"