# Camillo De Lellis

#15,066

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Italian mathematician

## Camillo De Lellis's AcademicInfluence.com Rankings

Camillo De Lellismathematics Degrees

Mathematics

#652

World Rank

#1201

Historical Rank

Measure Theory

#130

World Rank

#206

Historical Rank

Applied Mathematics

#309

World Rank

#334

Historical Rank

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Mathematics

## Camillo De Lellis's Degrees

- PhD Mathematics Scuola Normale Superiore di Pisa
- Bachelors Mathematics Scuola Normale Superiore di Pisa

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## Why Is Camillo De Lellis Influential?

(Suggest an Edit or Addition)According to Wikipedia, Camillo De Lellis is an Italian mathematician who is active in the fields of calculus of variations, hyperbolic systems of conservation laws, geometric measure theory and fluid dynamics. He is a permanent faculty member in the School of Mathematics at the Institute for Advanced Study. He is also one of the two managing editors of Inventiones Mathematicae.

## Camillo De Lellis's Published Works

### Published Works

- The Euler equations as a differential inclusion (2007) (522)
- On Admissibility Criteria for Weak Solutions of the Euler Equations (2007) (459)
- Estimates and regularity results for the DiPerna-Lions flow (2008) (286)
- Dissipative continuous Euler flows (2012) (273)
- Onsager's Conjecture for Admissible Weak Solutions (2017) (243)
- Global Ill‐Posedness of the Isentropic System of Gas Dynamics (2013) (203)
- Anomalous dissipation for 1/5-Hölder Euler flows (2015) (190)
- The $h$-principle and the equations of fluid dynamics (2011) (190)
- Dissipative Euler Flows and Onsager's Conjecture (2012) (166)
- Weak-Strong Uniqueness for Measure-Valued Solutions (2009) (152)
- The min--max construction of minimal surfaces (2003) (145)
- h -Principle and Rigidity for C 1, α Isometric Embeddings (2012) (135)
- Line energies for gradient vector fields in the plane (1999) (124)
- Dissipative Euler Flows with Onsager‐Critical Spatial Regularity (2014) (123)
- Rectifiable Sets, Densities and Tangent Measures (2008) (112)
- Q-valued functions revisited (2008) (105)
- Structure of Entropy Solutions for Multi-Dimensional Scalar Conservation Laws (2003) (100)
- Optimal rigidity estimates for nearly umbilical surfaces (2005) (99)
- Chapter 4 – Notes on Hyperbolic Systems of Conservation Laws and Transport Equations (2007) (74)
- Minimal entropy conditions for Burgers equation (2004) (72)
- Regularity of area minimizing currents III: blow-up (2013) (71)
- Ill-Posedness of Leray Solutions for the Hypodissipative Navier–Stokes Equations (2017) (69)
- SOME REMARKS ON THE THEORY OF ELASTICITY FOR COMPRESSIBLE NEOHOOKEAN MATERIALS (2002) (68)
- High dimensionality and h-principle in PDE (2016) (68)
- Regularity of area minimizing currents I: gradient Lp estimates (2013) (66)
- Regularity of area minimizing currents II: center manifold (2013) (59)
- Structure of entropy solutions to the eikonal equation (2003) (58)
- Well-Posedness for a Class of Hyperbolic Systems of Conservation Laws in Several Space Dimensions (2005) (57)
- A NOTE ON ADMISSIBLE SOLUTIONS OF 1D SCALAR CONSERVATION LAWS AND 2D HAMILTON–JACOBI EQUATIONS (2004) (54)
- The existence of embedded minimal hypersurfaces (2009) (53)
- On the Optimality of Velocity Averaging Lemmas (2003) (51)
- Almost-Schur lemma (2010) (51)
- A C0 Estimate for Nearly Umbilical Surfaces (2006) (51)
- On the chain rule for the divergence of BV-like vector fields: applications, partial results, open problems (2007) (49)
- A direct approach to Plateau's problem (2014) (49)
- Multiple valued functions and integral currents (2013) (48)
- Low-Regularity Solutions of the Periodic Camassa–Holm Equation (2007) (48)
- Sharp upper bounds for a variational problem with singular perturbation (2007) (46)
- Transporting microstructure and dissipative Euler flows (2013) (43)
- Existence of solutions for a class of hyperbolic systems of conservation laws in several space dimensions (2003) (42)
- On Turbulence and Geometry: from Nash to Onsager (2019) (42)
- ORDINARY DIFFERENTIAL EQUATIONS WITH ROUGH COEFFICIENTS AND THE RENORMALIZATION THEOREM OF AMBROSIO (2007) (40)
- Genus bounds for minimal surfaces arising from min-max constructions (2009) (40)
- Min-max theory for minimal hypersurfaces with boundary (2016) (38)
- Regularity Theory for 2-Dimensional Almost Minimal Currents II: Branched Center Manifold (2015) (34)
- Uniqueness of Tangent Cones for Two‐Dimensional Almost‐Minimizing Currents (2015) (34)
- Positive Solutions of Transport Equations and Classical Nonuniqueness of Characteristic curves (2020) (31)
- Regularity theory for $2$-dimensional almost minimal currents I: Lipschitz approximation (2015) (31)
- Existence of optimal strategies for a fire confinement problem (2009) (30)
- A NASH-KUIPER THEOREM FOR C1,/5−δ IMMERSIONS OF SURFACES IN 3 DIMENSIONS (2016) (30)
- The rectifiability of entropy measures in one space dimension (2003) (30)
- Some fine properties of currents and applications to distributional Jacobians (2002) (30)
- Performance level of an autonomous system of continuous monitoring of radioactivity in seawater. (2004) (30)
- The Generalized Caffarelli‐Kohn‐Nirenberg Theorem for the Hyperdissipative Navier‐Stokes System (2017) (29)
- Regularity theory for $2$-dimensional almost minimal currents III: Blowup (2015) (28)
- Regular selections for multiple-valued functions (2004) (28)
- Dissipative continuous Euler flows in two and three dimensions (2012) (26)
- Simple proof of two-well rigidity (2006) (26)
- A note on Alberti‘s rank-one theorem (2008) (26)
- The size of the singular set of area-minimizing currents (2015) (26)
- A direct approach to the anisotropic Plateau problem (2016) (23)
- A Nash–Kuiper theorem for $C^{1,\sfrac{1}{5}-\delta}$ immersions of surfaces in 3 dimensions (2015) (22)
- Oscillatory solutions to transport equations (2006) (22)
- Rectifiability and upper Minkowski bounds for singularities of harmonic $Q$-valued maps (2016) (22)
- A C⁰ estimate for nearly umbilical surfaces (2006) (20)
- Almgren's Q-valued Functions Revisited (2011) (20)
- Lower semicontinuous functionals for Almgren's multiple valued functions (2009) (20)
- Singular limit laminations, Morse index, and positive scalar curvature (2002) (19)
- Three circles theorems for Schrödinger operators on cylindrical ends and geometric applications (2007) (19)
- A quantitative compactness estimate for scalar conservation laws (2005) (19)
- A Regularizing Property of the 2D-Eikonal Equation (2014) (19)
- Higher integrability of the gradient for minimizers of the 2d Mumford–Shah energy (2013) (18)
- ORDINARY DIFFERENTIAL EQUATIONS WITH ROUGH COEFFICIENTS AND THE RENORMALIZATION THEOREM OF (2007) (18)
- ALLARD’S INTERIOR REGULARITY THEOREM: AN INVITATION TO STATIONARY VARIFOLDS (2017) (18)
- An example in the gradient theory of phase transitions (2002) (17)
- Continuous dissipative Euler flows and a conjecture of Onsager (2012) (17)
- Center Manifold: a case study (2011) (15)
- Regularity and Compactness for the DiPerna–Lions Flow (2008) (15)
- SBV Regularity for Hamilton-Jacobi Equations in R n (2010) (15)
- Remarks on the theory of elasticity (2003) (15)
- Lossless Analog Compression (2018) (14)
- On the boundary behavior of mass-minimizing integral currents (2018) (14)
- Polyconvexity equals rank-one convexity for connected isotropic sets in M2×2 (2003) (14)
- Some remarks on the distributional Jacobian (2003) (14)
- Hamilton Jacobi Equations with Obstacles (2011) (14)
- The h-principle and Onsager ’ s conjecture (2015) (14)
- On nonuniqueness of Hölder continuous globally dissipative Euler flows (2020) (13)
- Blowup of the BV norm in the multidimensional Keyfitz and Kranzer system (2005) (13)
- Regularity of area minimizing currents mod p (2019) (12)
- The regularity of minimal surfaces in higher codimension (2014) (12)
- Density lower bound estimates for local minimizers of the 2d Mumford–Shah energy (2013) (11)
- MCNP simulation and spectrum unfolding for an NaI monitor of radioactivity in aquatic systems (2007) (11)
- h-Principle and Rigidity for $C^{1,\alpha}$ Isometric Embeddings (2009) (11)
- Geometric measure theory and differential inclusions (2019) (11)
- Instability and nonuniqueness for the $2d$ Euler equations in vorticity form, after M. Vishik (2021) (11)
- C1, isometric embeddings of polar caps (2020) (11)
- The masterpieces of John Forbes Nash Jr (2016) (11)
- An extension of the identity Det=det (2010) (11)
- A note on the Hausdorff dimension of the singular set for minimizers of the Mumford–Shah energy (2014) (11)
- Higher integrability and approximation of minimal currents (2009) (10)
- SBV Regularity for Hamilton–Jacobi Equations in $${{\mathbb R}^n}$$ (2010) (10)
- Transport Equations and Multi-D Hyperbolic Conservation Laws (2008) (10)
- Min-max embedded geodesic lines in asymptotically conical surfaces (2016) (9)
- Ordinary differential equations with rough coefficients and the renormalization theorem of Ambrosio [after Ambrosio, DiPerna, Lions] (2008) (9)
- ODEs with Sobolev coefficients: The eulerian and the lagrangian approach (2008) (9)
- Partial regularity for mass-minimizing currents in Hilbert spaces (2018) (8)
- Anomalous Dissipation for the Forced 3D Navier–Stokes Equations (2022) (8)
- Area‐Minimizing Currents mod 2Q: Linear Regularity Theory (2019) (7)
- High resolution monitoring system for IRE stack releases. (2013) (6)
- Concentration estimates for entropy measures (2003) (6)
- Boundary Regularity of Mass-Minimizing Integral Currents and a Question of Almgren (2018) (6)
- Structure of entropy solutions: applications to variational problems (2002) (5)
- Weak stability and closure in turbulence (2021) (5)
- Neutron-photon discrimination and spectrum unfolding with a stilbene detector. (2010) (5)
- The Onsager theorem (2017) (5)
- Nonclassical minimizing surfaces with smooth boundary (2019) (5)
- Transport equations with integral terms: existence, uniqueness and stability (2016) (5)
- [Vascular accesses for hemodialysis]. (1979) (4)
- Anomalous dissipation for (2015) (4)
- John Forbes Nash Jr. (1928–2015) (2016) (4)
- Smoothing does not give a selection principle for transport equations with bounded autonomous fields (2020) (3)
- Hyperbolic equations and SBV functions (2010) (3)
- Fractional Sobolev regularity for the Brouwer degree (2017) (3)
- Gamma spectrum unfolding for a NaI monitor of radioactivity in aquatic systems. (2010) (3)
- An Allard-type boundary regularity theorem for $2d$ minimizing currents at smooth curves with arbitrary multiplicity (2021) (3)
- THE GEOMETRY OF C1,α FLAT ISOMETRIC IMMERSIONS (2020) (2)
- Sharp rigidity estimates for nearly umbilical surfaces (2003) (2)
- Onsager critical solutions of the forced Navier-Stokes equations (2022) (2)
- $C^{1,\alpha}$ Isometric Embeddings of Polar Caps (2018) (2)
- Lossless linear analog compression (2016) (2)
- Area minimizing hypersurfaces modulo $p$: a geometric free-boundary problem (2021) (2)
- The regularity theory for the area functional (in geometric measure theory) (2021) (2)
- Endpoint regularity for 2d Mumford-Shah minimizers: On a theorem of Andersson and Mikayelyan (2020) (2)
- Year : 2007 On the chain rule for the divergence of BV-like vector fields : applications , partial results (2010) (2)
- Transport equation with integral terms (2016) (2)
- Endpoint regularity of $2$d Mumford-Shah minimizers (2015) (1)
- Two-dimensional almost area minimizing currents (2016) (1)
- Dirichlet energy-minimizers with analytic boundary (2019) (1)
- On the spectral distribution of certain sequences of band matrices (2001) (1)
- A regularizing property of the 2 D-eikonal equation (2017) (1)
- The Nash–Kuiper Theorem and the Onsager Conjecture (2020) (1)
- Surprising solutions to the isentropic Euler system of gas dynamics (2014) (1)
- Uniqueness of boundary tangent cones for 2-dimensional area-minimizing currents (2021) (1)
- Min-max embedded geodesic lines and a question of Bangert (2016) (0)
- Partial Differential Equations (2018) (0)
- elasticity for compressible Neohookean materials (2002) (0)
- Two-dimensional almost area minimizing currents (2016) (0)
- The geometry of $C^{1,\alpha}$ flat isometric immersions (2020) (0)
- Fine structure of the singular set of area minimizing hypersurfaces modulo $p$ (2022) (0)
- Regularity Theory for 2-Dimensional Almost Minimal Currents II: Branched Center Manifold (2017) (0)
- Density lower bound estimates for local minimizers of the 2d Mumford–Shah energy (2013) (0)
- Almgren's center manifold in a simple setting (2018) (0)
- The chain rule for the divergence of BV-like vector fields (2006) (0)
- Regularity of area minimizing currents I: gradient Lp estimates (2014) (0)
- Ultra sensitive sea water radioactivity monitoring system (2003) (0)
- In Memoriam John Forbes Nash Jr. (2016) (0)
- Calculus of Variations Simple proof of two-well rigidity (2006) (0)
- Dissipative continuous Euler flows (2012) (0)
- Almgren’s center manifold in a simple setting (2020) (0)
- The Masterpieces of John Forbes Nash Jr. (2019) (0)
- Smoothing does not give a selection principle for transport equations with bounded autonomous fields (2021) (0)
- applications to variational problems (2002) (0)
- Transport equations with integral terms: existence, uniqueness and stability (2016) (0)
- The fine structure of the singular set of area-minimizing integral currents I: the singularity degree of flat singular points (2023) (0)
- [Our experience in perforated gastroduodenal ulcer]. (1980) (0)
- 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) (0)
- Partial Differential Equations An extension of the identity Det = det Une extension de l ’ identité Det = det (2010) (0)
- Ill-posedness for Bounded Admissible Solutions of the 2-dimensional p-system (2008) (0)
- 2-DIMENSIONAL ALMOST AREA MINIMIZING CURRENTS (2015) (0)
- Ill-Posedness of Leray Solutions for the Hypodissipative Navier–Stokes Equations (2018) (0)
- C. De Lellis - Center manifolds and regularity of area-minimizing currents (Part 1) (2015) (0)
- 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) (0)
- EXISTENCE OF SOLUTIONS FOR A CLASS OF HYPERBOLICSYSTEMS OF CONSERVATION LAWS IN SEVERAL (2003) (0)
- ISOMETRIC EMBEDDINGS OF POLAR CAPS (0)
- [Total gastrectomy in the treatment of gastric carcinoma]. (1980) (0)
- Demonstration of equipment: Ultra sensitive sea water radioactivity monitoring system autonomous low power consumption equipped with wireless data communication (2002) (0)
- Year : 2011 SBV regularity for Hamilton-Jacobi equations in (2019) (0)
- [Familial polyposis and cancer. Apropos of 4 cases]. (1980) (0)
- GEOMETRIC STRUCTURE OF MIGDAL’S CONSTRAINED VORTEX SURFACES (2022) (0)

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## What Schools Are Affiliated With Camillo De Lellis?

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