[PDF] Top 20 On quasi-reversibility solutions to the Cauchy problem for the Laplace equation: regularity and error estimates

... The objective is now to study the regularity of the solution (u ε , λ ε ) to problem ( 7 ) and to complete the statements ( 9 ) and ( 10 ) of ... Voir le document complet

... as to have an amplitude of size η). Jochmann showed in [22] the weak convergence of the corresponding solutions to the Maxwell-Landau-Lifschitz system towards the ... Voir le document complet

... kernels, Cauchy theory in exponentially weighted spaces, regularity of the solutions ...underline the fact that Theorem 1.1 largely improves previous results on the Cauchy ... Voir le document complet

... estimation for the Helmholtz equation Early work in 1D, with first-order FE: ...Strouboulis and S.K. Gangaraj, Int. J. Numer. Meth. Engrg., 1997: A posteriori error estimation ... Voir le document complet

... A-priori estimates. We start with the observation that some properties of the solution to the original problem ( 1 ), or its time discrete counterpart, are not preserved by ... Voir le document complet

... Gressman and Strain [18] in parallel with Alexan- dre et ...a Cauchy theory in spaces of type H n x H v ℓ (µ −1/2 ). One of the famous difficulty of the Boltzmann equation without ... Voir le document complet

... like to stress that the complete dynamics of (GP) exhibits a remarkable variety of special solutions and ...Besides the already mentioned stationary vortices, there are also soliton ... Voir le document complet

... consider the problem of numerically approximating the solution of an elliptic partial dierential equation with random coecients and homogeneous Dirichlet boundary ...on the ... Voir le document complet

... . (3.8) Thus, (3.4) follows from (3.8) by taking ε = |λ 2 − λ 1 |. To prove (3.7) we will make use of (3.5) with j = j 0 + 2. If j 0 < k 0 we have j ≤ k 0 + 1 and hence this case can be treated in ... Voir le document complet

... of the original problem, due to the lack of ...Anyway, the related stress fields ∇F (∇u n ) still weakly converge, to a limit stress field of the form ∇H ∗ (∇u 0 ), with u ... Voir le document complet

... of the key ingredients in many of the more recent above-mentioned references is the multivariate Stein’s ...in the multivariate CLT were first obtained Stein’s method by Barbour in [1] (see ... Voir le document complet

... a) and by Cξ −3 in case b). This concludes the proof of ...since the integral kernel G = (G r , G z ) in (22) satisfies the same bound as the two- dimensional Biot-Savart kernel in R 2 ... Voir le document complet

... and Wang [ 12 ]. We seek to approximate equation ( ...existence for these systems and use energy methods to show that the time of existence is independent of ε and ... Voir le document complet

... 10 The level-set approach is a very convenient tool in shape identification, see [29] for a general introduction, or [30] where the approach is applied to detect obstacles in a Stokes ...flow. ... Voir le document complet

... 1,α regularity result is internal; therefore in Theorem ...any regularity for ∂Ω. On the other hand, as mentioned earlier, to prove our Ahlfors-regularity result, we required Ω ... Voir le document complet

... takes the dispersion of the velocities in the orthogonal to the z -direction plane as well as the self-consistent nonlinear interaction into account, which seems to be ... Voir le document complet

... in the sense that a fixed fraction of these points are located on the boundary ...experiments. The rest of this paper is organized as follow: we give a brief account in §2 on approximation of ... Voir le document complet

... order to obtain an estimate of λ 1,β , we look into the strategies used for the extremal problems, which are the Steklov (β = 0) and the Laplace-Beltrami (β → +∞) ... Voir le document complet

... of the paper is the ...notation and then prove a few more or less standard elliptic ...give the definition and first properties of the Poisson point process and then prove ... Voir le document complet

... For the Boltzmann equation estimate ( ...in the model, the local in time estimate obtained in [ 26 ] which reads I(f (t)) 6 e c t 2I(f 0 ) + c (1 + t 3 )
, for some explicit c ... Voir le document complet