@Article{IJNAM-5-109,
author = {Meier , S. and Böhm , M.},
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 = {2018},
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/},
url = {http://global-sci.org/intro/article_detail/ijnam/843.html}
}