Comptes Rendus

Special Issue

From Generation to Generation: The Mathematical Legacy of Haïm Brezis

All articles

Research article - Dynamical systems
Equidistribution of continuous low-lying pairs of horocycles via Ratner’s theorem
p. 1-5
Research article - Geometry and Topology
The second coefficient of the Alexander polynomial as a satellite obstruction
p. 7-11
Research article - Partial differential equations
On selection dynamics for a nonlocal phenotype-structured model
p. 13-27
Research article - Operator theory
A Sharp Entropy Condition for the Density of Angular Derivatives
p. 29-33
Research article - Functional analysis, Probability theory
The Mandelbrot–Kahane problem of Benoît Mandelbrot model of turbulence
p. 35-41
Research article - Geometry and Topology
Pirashvili–Richter-type theorems for the reflexive and dihedral homology theories
p. 43-55
Research article - Number theory
Fractional dimension of some exceptional sets in continued fractions
p. 57-68
Research article - Partial differential equations, Geometry and Topology
Monotonicity for quasilinear elliptic problems with a sign-changing nonlinearity in half-planes
p. 69-87
Research article - Geometry and Topology, Group theory
Burau representation of $B_4$ and quantization of the rational projective plane
p. 89-107
Research article - Geometry and Topology
Convexity of space-like projections of submanifolds with co-dimension 2 in Lorentz–Minkowski space
p. 109-113
Research article - Numerical analysis
Stability estimates for solving Stokes problem with nonconforming finite elements
p. 115-137
Research article - Partial differential equations, Mathematical physics
Uniqueness for the Camassa–Holm equation with non-homogeneous boundary conditions
p. 139-168
Research article - Geometry and Topology, Representation theory
Betti Tate’s thesis and the trace of perverse schobers
p. 169-181
Research article - Mathematical physics, Probability theory
A simple construction of the Anderson operator via its quadratic form in dimensions two and three
p. 183-197
Research article - Functional analysis
Operator algebraic characterization of the noncommutative Poisson boundary
p. 199-204
Research article - Algebra, Geometry and Topology
Adjoints, wrapping, and morphisms at infinity
p. 205-212
Research article - Algebraic geometry
Hodge–Lyubeznik numbers
p. 213-221
Research article - Probability theory
Reflected BSDEs with default time and irregular obstacles
p. 223-233
Research article - Algebra, Combinatorics
Reflections and quotients in Coxeter groups
p. 235-239
Research article - Control theory
A new look at the controllability cost of linear evolution systems with a long gaze at localized data
p. 241-266
Research article - Group theory
On the nilpotency of locally pro-$p$ contraction groups
p. 267-270
Research article - Partial differential equations
On the existence of degenerate solutions of the two-dimensional $H$-system
p. 271-281
Research article - Partial differential equations
Multi-solitary waves for the one-dimensional Zakharov system
p. 283-321
Research article - Combinatorics
About Berge–Füredi’s conjecture on the chromatic index of hypergraphs
p. 323-328
Research article - Combinatorics, Number theory
The number system in rational base $3/2$ and the $3x+1$ problem
p. 329-336
Research article - Geometry and Topology
Geodesic orbit and weakly symmetric spray manifolds
p. 337-344
Research article - Partial differential equations
Anomalous dissipation for the d-dimensional Navier–Stokes equations
p. 345-351
Research article - Partial differential equations
Uniqueness of positive solutions to fractional nonlinear elliptic equations with harmonic potential
p. 353-363
Research article - Control theory
A linear test for global nonlinear controllability
p. 365-375
Research article - Functional analysis, Harmonic analysis
Relatively bounded and relatively trace class perturbations
p. 377-382
Research article - Algebra
Azumaya locus over certain quantum symplectic spaces II
p. 383-405
Research article - Partial differential equations
Lower semicontinuity of nonlocal $L^\infty $ energies on $SBV_0(I)$
p. 407-414
Research article - Mathematical logic
A metric lifting theorem
p. 415-424
Research article - Dynamical systems
On the point spectrum of quasi-periodic Schrödinger operators
p. 425-428
Research article - Algebraic geometry, Geometry and Topology
The (co)homology of the Deligne–Mumford moduli spaces of marked rational curves
p. 429-436
Research article - Dynamical systems
Markov partitions for non-transitive expansive flows
p. 437-444
Research article - Complex analysis and geometry
On quasiconformal extension of harmonic mappings with nonzero pole
p. 445-454
Research article - Probability theory
Non-uniform Berry–Esseen bounds via Malliavin–Stein method
p. 455-463
Research article - Number theory
Trivialité des groupes de Whitehead réduits avec applications à l’approximation faible et l’approximation forte
[Triviality of reduced Whitehead groups with applications to weak approximation and strong approximation]
p. 465-477
Research article - Partial differential equations
Existence of an extremal function of critical Sobolev embedding with an $\alpha $-homogeneous weight
p. 479-485
Research article - Algebraic geometry
A non-vanishing conjecture for cotangent bundles on elliptic surfaces
p. 487-497
Research article - Partial differential equations
A note on contractive semi-groups on a 1:1 junction for scalar conservation laws and Hamilton–Jacobi equations
p. 499-510
Research article - Complex analysis and geometry, Algebraic geometry
Toric polar maps, normal crossings and mixed volumes
p. 511-522
Research article - Algebraic geometry
The affine Grassmannian as a presheaf quotient
p. 523-532
Research article - Partial differential equations
Hessian regularity in Hölder spaces for a semi-linear bi-Laplacian equation
p. 533-539
Research article - Algebra, Number theory
Normal points on Artin–Schreier curves over finite fields
p. 541-554
Research article - Dynamical systems
Iteration of exponentials with sign changes
p. 555-564
Research article - Geometry and Topology
The isospectral problem for $p$-widths: an application of Zoll metrics
p. 565-570
Research article - Partial differential equations
Liouville theorems for $p$-Laplace equations with critical Hardy–Hénon exponents
p. 571-582
Research article - Partial differential equations
On gelation for the Smoluchowski coagulation equation
p. 583-591
Research article - Algebraic geometry
The cuspidal cubic and line arrangements with only triple points
p. 593-598
Research article - Harmonic analysis
A direct proof of the weighted Pólya–Knopp inequality following Carleson’s method
p. 599-602
Research article - Complex analysis and geometry
Fubini–Study forms on punctured Riemann surfaces
p. 603-615
Research article - Probability theory
Wong–Zakai approximations and support theorems for SDEs under Lyapunov conditions
p. 617-628
Research article - Functional analysis
On zero eigenvalue of invariant Schrödinger operators with point interactions at vertices of some regular polyhedra
p. 629-639
Research article - Algebra
Cohomology and deformations of modified Rota–Baxter Lie–Yamaguti algebras
p. 641-662
Research article - Statistics
An infinite-dimensional Christoffel function and detection of abnormal trajectories
p. 663-676
Research article - Partial differential equations
Another look at qualitative properties of eigenvalues using effective Hamiltonians
p. 677-693
Research article - Geometry and Topology, Spectral theory
On Berger’s isoperimetric problem
p. 695-704
Research article - Algebra
Balancedness of complete cohomology with respect to subcategories
p. 705-722
Research article - Algebra
Automorphism group of $\bar{B}$
p. 723-737
Research article - Numerical analysis
Approximate D-optimal design and equilibrium measure
p. 739-756
Research article - Probability theory
Non-uniform Berry–Esseen bounds for exchangeable pairs with applications to the mean-field classical $N$-vector models and Jack measures
p. 757-776
Research article - Algebra
Kashiwara–Vergne solutions degree by degree
p. 777-789
Erratum - Dynamical systems
Corrigendum to “The critical exponent functions”
p. 791-792
Research article - Probability theory
Every recurrent network has a potential tending to infinity
p. 793-798
Research article - Algebraic geometry
Teissier singularities
p. 799-808
Research article - Numerical analysis
Point-set registration in bounded domains via the Fokker–Planck equation
p. 809-824
Research article - Algebra, Dynamical systems
Irrationality of the length spectrum
p. 825-828
Historical Commentary - Algebra
Grothendieck and differential calculus
p. 829-841
Erratum - Algebraic geometry, Singularity theory
Corrigendum to “Hodge–Lyubeznik numbers”
p. 843-844
Research article - Dynamical systems
Bedford–McMullen carpets meet nonlinear curves
p. 845-851
Research article - Functional analysis
Factoriality of twisted locally compact group von Neumann algebras
p. 853-859
Research article - Algebra
On the width of $\sigma $-subnormality in finite groups
p. 861-866
Research article - Algebraic geometry, Number theory
Isogeny and overconvergence
p. 867-871
Research article - Algebraic geometry, Number theory
Generalised André–Pink–Zannier conjecture for Shimura varieties of abelian type
p. 873-878
Research article - Functional analysis
Cyclicity of composition operators on the Paley–Wiener spaces
p. 879-886
Research article - Partial differential equations
A short proof of the $C^{1,1}$ regularity for the eikonal equation

p. 887-891
Research article - Control theory, Partial differential equations
Some fundamental properties of the approximate synchronization by groups for a coupled system of wave equations with internal controls
p. 893-904
Research article - Probability theory
A note on the compact uniform integrability in metric spaces
p. 905-916
Research article - Singularity theory
Atypical values at infinity of real polynomial maps with $2$-dimensional fibers
p. 917-932
Research article - Group theory
Semi-extraspecial $p$-groups with automorphisms of large order
p. 933-940
Research article - Number theory
Small gaps in the Ulam sequence
p. 941-949
Research article - Dynamical systems, Group theory
Groups acting on the line with at most 2 fixed points: an extension of Solodov’s theorem
p. 951-958
Research article - Complex analysis and geometry
Analytic and asymptotic properties of solutions to a non-homogeneous functional differential equation
p. 959-975
Research article - Probability theory
On cases where Litt’s game is fair
p. 977-984
Research article - Number theory
Note on a symmetric Diophantine equation
p. 985-988
Research article - Algebra, Algebraic geometry
Regularity of semi-valuation rings and homotopy invariance of algebraic K-theory
p. 989-1001
Research article - Mathematical logic
Magidor-like forcing and the cofinality of the Galvin number
p. 1003-1011
Research article - Partial differential equations
Uniform regularity and weight estimates for the Poisson problems when rounding off the conical points
p. 1013-1023
Research article - Functional analysis, Geometry and Topology
Obstacles for Sobolev-homeomorphisms with low rank: pointwise a.e. vs distributional Jacobians
p. 1025-1033
Research article - Statistics
Rates of strong uniform consistency for the $k$-nearest neighbors kernel estimators of density and regression function
p. 1035-1046
Research article - Complex analysis and geometry
Asymptotic behaviour of Bohr’s radii for polynomials on simply connected domains
p. 1047-1058
Research article - Algebraic geometry
A remark on the effective nonvanishing of Calabi–Yau varieties
p. 1059-1063
Research article - Complex analysis and geometry
New eigenfunctions for the negative part of the Connes–Moscovici prolate spectrum
p. 1065-1081
Research article - Numerical analysis, Partial differential equations
Asymptotic optimality of the edge finite element approximation of the time-harmonic Maxwell’s equations
p. 1083-1101
Research article - Functional analysis, Probability theory
On cutoff via rigidity for high dimensional curved diffusions
p. 1103-1121
Research article - Representation theory
A functorial approach to $n$-abelian categories
p. 1123-1175
Research article - Partial differential equations
A dynamical system approach to the Chandrasekhar–Hamilton–Jacobi equation

p. 1177-1217
Research article - Partial differential equations
Gluing instantons à la Brezis–Coron in dimension four and the dipole construction

p. 1219-1261
Research article - Partial differential equations
Weakly elliptic damping gives sharp decay
p. 1263-1275
Research article - Partial differential equations
Nonvariational double phase problems with variable exponents depending on the gradient of the solution with convection term
p. 1277-1287
Research article - Control theory
The independent isolation number of a tree
p. 1289-1299
Research article - Partial differential equations
Electron beams: partially flat solutions of a nonlinear elliptic equation with a singular absorption term

p. 1301-1338
Research article - Partial differential equations
A new proof of a Liouville theorem for the one dimensional Gross–Pitaevskii equation

p. 1339-1350
Research article - Combinatorics, Harmonic analysis
Spherical sets avoiding orthonormal bases
p. 1351-1362
Research article - Harmonic analysis
Quantitative suboptimal Sobolev embeddings

p. 1363-1376
Research article - Partial differential equations
Recovering functions via doubly homogeneous nonlocal gradients

p. 1377-1406