The boundary behavior of a composite material
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 3, p. 407-435

In this paper, we study how solutions to elliptic problems with periodically oscillating coefficients behave in the neighborhood of the boundary of a domain. We extend the results known for flat boundaries to domains with curved boundaries in the case of a layered medium. This is done by generalizing the notion of boundary layer and by defining boundary correctors which lead to an approximation of order ε in the energy norm.

On étudie ici le comportement au voisinage de la frontière du domaine de solutions de problèmes elliptiques à coefficients oscillant périodiquement. Les résultats, connus pour des frontières plannes, sont étendus au cas de frontières courbes et pour un milieu stratifié. On généralise pour cela la notion de couche limite et on définit des correcteurs de frontière qui conduisent à une approximation d’ordre ε dans la norme énergie.

Classification:  35B27,  35B40
Keywords: homogenization, generalized boundary layers, energy error estimates
@article{M2AN_2001__35_3_407_0,
     author = {Neuss-Radu, Maria},
     title = {The boundary behavior of a composite material},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {3},
     year = {2001},
     pages = {407-435},
     zbl = {0985.35092},
     mrnumber = {1837078},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2001__35_3_407_0}
}
Neuss-Radu, Maria. The boundary behavior of a composite material. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 3, pp. 407-435. http://www.numdam.org/item/M2AN_2001__35_3_407_0/

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