We invenstigate a local analysis of the Lavrentiev regularization method applied to the ill-posed Cauchy problem. A convergence analysis of the approximated solution is carried out in a sub region away from the incomplete boundary, which is the source of the instability of the Cauchy solution. The use of a Carleman estimate with boundary condition by D.Tataru (see [4]) brings about super-conver...

We introduce the poly-Cauchy polynomials which generalize the classical Cauchy polynomials, and investigate their arithmetical and combinatorial properties. These polynomials are considered as analogues of the poly-Bernoulli polynomials that generalize the classical Bernoulli polynomials. Moreover, we investigate the zeta functions which interpolate the poly-Cauchy polynomials. The values of th...

BD-N is a weak principle of constructive analysis. Several interesting principles implied by BD-N have already been identified, namely the closure of the anti-Specker spaces under product, the Riemann Permutation Theorem, and the Cauchyness of all partially Cauchy sequences. Here these are shown to be strictly weaker than BD-N, yet not provable in set theory alone under constructive logic. keyw...

We prove that the space-time developments of generic solutions of the vacuum constraint Einstein equations do not possess any global or local Killing vectors, when Cauchy data are prescribed on an asymptotically flat Cauchy surface, or on a compact Cauchy surface with mean curvature close to a constant, or for CMC asymptotically hyperbolic initial data sets. More generally, we show that non-exi...

The Cauchy problem is studied for an homogeneous quantum kinetic equation describing the Compton effect. Since the collision kernel commonly used in physics is highly singular, numerical simulations are performed for related collision kernels to get a preliminary insight into the behavior of the solutions. Some of the numerical results are then given a theoretical explanation. Global existence ...

Cauchy coeecient integrals and Hankel contours provide a natural generalization of Stirling numbers for unrestricted complex values of their arguments. Many classical identities survive such an extension. Sur les nombres de Stirling d'indice complexe et les contours de Hankel R esum e : Les int egrales de Cauchy et les contours de Hankel fournissent une g en eralisation naturelle des nombres de...

In this paper, we develop two piecewise polynomial methods for the numerical evaluation of Cauchy Principal Value integrals of oscillatory kind. The two piecewisepolynomial quadratures are compact, easy to implement, and are numerically stable. Two numerical examples are presented to illustrate the two rules developed, The convergence of the two schemes is proved and some error bounds obtai...