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Nous étudions dans cet article des espaces de moyennes définis par une méthode discrète d'interpolation. Après avoir démontré leur coïncidence, dans le cas général, avec les espaces$(A$_{o}, A_{1})_{Q; J}et$(A$_{0}, A_{1})_{Q;K}de C. Bennett ([3]), nous obtenons simplement les théorèmes de dualité en utilisant la méthode de [2] et aussi les arguments de [7]. Nous remercions le rapporteur dont les conseils nous ont permis en particulier de simplifier nos démonstrations.

The Burton-Cabrera-Frank (BCF) model for the flow of line defects (steps) on crystal surfaces has offered useful insights into nanostructure evolution. This model has rested on phenomenological grounds. Our goal is to show via scaling arguments the emergence of the BCF theory for noninteracting steps from a stochastic atomistic scheme of a kinetic restricted solid-on-solid model in one spatial dimension. Our main assumptions are: adsorbed atoms (adatoms) form a dilute system, and elastic effects of the crystal lattice are absent. The step edge is treated as a front that propagates via probabilistic rules for atom attachment and detachment at the step. We formally derive a quasistatic step flow description by averaging out the stochastic scheme when terrace diffusion, adatom desorption, and deposition from above are present.

We show existence and uniqueness of solutions to the Monge-Ampere equation on compact almost complex manifolds with non-integrable almost complex structure.

In this paper, we derive an a-posteriori error indicator for the Generalized Multiscale Finite Element Method (GMsFEM) framework. This error indicator is further used to develop an adaptive enrichment algorithm for the linear elliptic equation with multiscale high-contrast coefficients. The GMsFEM, which has recently been introduced in [13], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space,(2) the construction of the offline space, and (3) the construction of the online space (the latter for parameter-dependent problems). In [13], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we