Showing papers in "Comptes Rendus Mathematique in 2010"

TL;DR: This paper showed that there exist exactly 50 fake projective planes up to homeomorphism and 100 up to biholomorphism, and exhibited each of them explicitly as a quotient of the unit ball in C 2.

TL;DR: In this article, the Herglotz wave function with kernel was shown to be the Tikhonov regularized solution of the far eld equation, and it was shown that it is also the kernel regularized Herglots wave function.

TL;DR: In this paper, a non-anticipative pathwise calculus for functionals of a Brownian semimartingale and its quadratic variation is developed and a functional Ito formula is obtained for locally Lipschitz functionals.

TL;DR: In this paper, the main theorem of Morales, Ramis and Simo (2007) about Galoisian obstructions to meromorphic integrability of Hamiltonian systems can be naturally extended to the non-Hamiltonian case.

TL;DR: In this paper, the authors extend the Reilly formula for drifting Laplacian operators and apply it to study eigenvalue estimate for drifting LPA operators on compact Riemannian manifolds' boundary.

TL;DR: In this article, it was shown that if the generic Sherrington-Kirkpatrick Hamiltonian contains a p-spin term then the Ghirlanda-Guerra identities for the pth power of the overlap hold in strong sense without averaging.

TL;DR: In this article, it was shown that two self-similar sets E A and E B are Lipschitz equivalent if and only if # A = # B and # B = # A + a n.

TL;DR: The bound is computed ''oine" and is valid over the entire parameter domain; it is thus readily employed in (say) the \online" reduced basis context.

TL;DR: In this paper, the authors prove uniqueness of measure-valued solutions and L p -solutions to degenerate second order Fokker-Planck equations under weak conditions on the coefficients.

TL;DR: In this article, the authors studied the properties of solutions to a linear evolution equation perturbed by a cylindrical Levy process and found that solutions, under rather weak requirements, do not have a cadlag modification.

TL;DR: In this article, a new type of Stirling series, which extends the Gosper's formula for big factorials, was constructed, and sharp inequalities for the gamma and digamma functions were established.

TL;DR: In this paper, the authors present a nouvelle formulation of the Asymptotic Preserving (AP) strategy for schemas numeriques, based on the decomposition micro-macro de la fonction distribution.

TL;DR: In this paper, a Carleman estimate for the one-dimensional degenerate parabolic equation v t + (x α v x ) x − b ( x, t ) v + ( x β / 2 c ( x, t) v ) x = 0.

TL;DR: In this article, the authors present global L p boundedness results for Fourier integral operators in R n, where the main question is what are the decay conditions on the amplitudes for the operators to be bounded on L p (R n ).

TL;DR: In this paper, a new direction splitting-based fractional time stepping method was introduced for solving the Navier-Stokes equations, where the pressure correction is computed by solving a sequence of one-dimensional elliptic problems in each spatial direction.

TL;DR: This work construct the coarse grid space using the low frequency modes of the subdomain DtN (Dirichlet-Neumann) maps, and applies the obtained two-level preconditioner to the linear system arising from an overlapping domain decomposition.

TL;DR: In this paper, a generalized system of ODE's was used to model a finite number of biological populations in a competitive interaction, and the convergence to a unique stable equilibrium was proved.

TL;DR: In this paper, the existence and uniqueness of p-integrable solutions to multidimensional backward stochastic differential equations (BSDEs) with super-linear growth coefficient and a p-Integrable terminal condition (p > 1 ) were established.

TL;DR: For the first time, an explicit closed form expression for the characteristic function of the generalized normal distribution (GND) was derived in this paper, and the correlation coefficient between variate-values and their ranks in samples from the GND was derived.

TL;DR: In this paper, renormalized solutions for the problems of the kind β(u)+(−)s/2u f in Rn,======¯¯¯¯f ∈ L1(Rn) were defined.

TL;DR: The authors decrivons a technique non lineaire which permet de supprimer les oscillations apparaissant pour la discretisation d'operateur de diffusion avec des schemas volumes finis centres sur les mailles.

TL;DR: In this article, the authors show that under suitable conditions on the data, they can construct a sequence of solutions of the second grade fluid that converges to the probabilistic strong solution of the stochastic Navier-Stokes equations when the stress modulus α tends to zero.

TL;DR: In this article, a new fictitious domain model for the Brinkman or Stokes/Brinkman problems was proposed to handle general jump embedded boundary conditions on an immersed interface.

TL;DR: In this paper, the Liouville type result for smooth positive solutions to the Lichnerowicz equation in R n was shown for a complete Riemannian manifold with the Ricci curvature bounded from below.

TL;DR: In this article, a three field mixed formulation for solving the Stokes problem with Tresca-type nonlinear boundary conditions is proposed and studied. And two Lagrange multipliers are used to enforce div ( u ) = 0 constraint and to regularize the energy functional.

TL;DR: In this article, the authors consider a linear Schrodinger equation with bilinear control and prove the convergence of the whole solution, as t → + ∞, using control Lyapunov functions and an adaptation of the LaSalle invariance principle.

TL;DR: In this article, the equivalence between the optimality of a transport plan for the Monge-Kantorovich problem and the condition of c-cyclical monotonicity was investigated.

TL;DR: In this article, it was shown that if g is continuous, monotonic and has a general growth in y, g is uniformly continuous in z, and ( g ( t, 0, 0 ) ) t ∈ [ 0, T ] is square integrable, then for each square integrinable terminal condition ξ, the one-dimensional backward stochastic differential equation with the generator g has a unique solution.

TL;DR: In this paper, a methode for calculer au premier ordre le comportement homogeneise d'un milieu consistant en un materiau periodique de reference perturbe de maniere stochastique.

TL;DR: Time-dependent statistical solutions of the three-dimensional Navier–Stokes equations for incompressible fluids are considered and a new formulation of one of them is given, and an existence proof for this new formulation is given.