Mathematical Methods in The Applied Sciences 

About: Mathematical Methods in The Applied Sciences is an academic journal published by Wiley. The journal publishes majorly in the area(s): Boundary value problem & Nonlinear system. It has an ISSN identifier of 0170-4214. Over the lifetime, 9001 publications have been published receiving 100095 citations.

Vector potentials in three-dimensional non-smooth domains

Abstract: On presente dans cet article un certain nombre de resultats concernant le potentiel vecteur associe a une fonction a divergence nulle dans un ouvert borne de dimension trois. En particulier, plusieurs types de conditions aux limites sont proposes, pour lesquels on discute l'existence, l'unicite et la regularite du potentiel vecteur. On analyse la convergence d'une discretisation par elements finis de ces potentiels et on indique une application concernant l'approximation de fluides visqueux incompressibles.

Thin elastic and periodic plates

Abstract: This paper is devoted to the study of a three dimensional model of elastic periodic plate when the thickness e of the plate and the size ω of the periods are small. In the three studied limits (e 0 then ω 0), (ω 0 then e 0) and lately (e and ω 0 together) the three dimensional equation of elasticity are approached by the two dimensional general equations of a linear anisotropic plate, the stretching and bending being coupled. This study points out the importance of the ratio of the two small parameters, indeed the moduli occuring in the two dimensional equations are different in the three limits. In each case a convergence proof is carried out.

On the boundary value problem of the biharmonic operator on domains with angular corners

Abstract: The paper is concerned with boundary singularities of weak solutions of boundary value problems governed by the biharmonic operator. The presence of angular corner points or points at which the type of boundary condition changes in general causes local singularities in the solution. For that case the general theory of V. A. Kondrat'ev provides a priori estimates in weighted Sobolev norms and asymptotic singular representations for the solution which essentially depend on the zeros of certain transcendental functions. The distribution of these zeros will be analysed in detail for the biharmonic operator under several boundary conditions. This leads to sharp a priori estimates in weighted Sobolev norms where the weight function is characterized by the inner angle of the boundary corner. Such estimates for “negative” Sobolev norms are used to analyse also weakly nonlinear perturbations of the biharmonic operator as, for instance, the von Karman model in plate bending theory and the stream function formulation of the steady state Navier-Stokes problem. It turns out that here the structure of the corner singularities is essentially the same as in the corresponding linear problem.

A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains

Abstract: Let ~ u be a vector field on a bounded Lipschitz domain in R 3 , and let ~ u together with its divergence and curl be square integrable. If