@Article{IJNAM-5-5,
author = {S., Meier and M., Böhm},
title = {A Note on the Construction of Function Spaces for Distributed-Microstructure Models with Spatially Varying Cell Geometry},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2008},
volume = {5},
number = {5},
pages = {109--125},
abstract = {<p style="text-align: justify;">We construct Lebesgue and Sobolev spaces of functions
defined on a continuous distribution of domains {$Y_x \subset \mathbb{R}^m$ : $x \in \Omega$}. The resulting spaces can be viewed as a
generalisation of the Bochner spaces $L_p(\Omega;W_q^l(Y))$ for the case
that $Y$ depends on $x \in \Omega$. Furthermore, we introduce a
Lebesgue space of functions defined on the boundaries {$∂Y_x : x \in \Omega$}. The latter construction
relies on a uniform Lipschitz parametrisation of the above collection of
boundaries, interpreted as a higher-dimensional manifold. The results
are applied to prove existence, uniqueness and upper and lower bounds
for a distributed-microstructure model of reactive transport in a
heterogeneous porous medium.</p>},
issn = {2617-8710},
doi = {https://doi.org/2008-IJNAM-843},
url = {https://global-sci.com/article/83746/a-note-on-the-construction-of-function-spaces-for-distributed-microstructure-models-with-spatially-varying-cell-geometry}
}