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| We study some questions of analysis in view of the modeling of tree-like structures, such as the human lungs. More particularly, we focus on a class of planar ramified domains whose boundary contains a fractal self-similar part, noted $\Gamma$.
We first study the Sobolev regularity of the traces on the fractal part $\Gamma$ of the boundary of functions in some Sobolev spaces of the ramified domains. Then, we study the existence of Sobolev extension operators for the ramified domains we consider. In particular, we show that there exists $p*\in(1,\infty)$ such that there are $W^{1,p}$-extension operator for the ramified domains for every $1 |
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