Geodesic
The $p$-Laplacian in domains with small random holes
Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 2, pp. 435-458

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We investigate sequences of nonlinear Dirichlet problems of the form \begin{equation*} \tag{$P_h$} \begin{cases} -\text{div}\,(|Du_{h}|^{p-2} Du_{h})=g, \ \text{in } D \setminus E_{h} \\ u_{h}\in H^{1,p}_{0}(D \setminus E_{h}). \end{cases} \end{equation*} where $2\leq p \leq n$ and $E_{h}$ are random subsets of a bounded open set $D$ of $\mathbb{R}^{n}$$(n\geq 2)$. By means of a variational approach, we study the asymptotic behaviour of solutions of $(P_h)$, characterizing the limit problem for suitable sequences of random sets. 
@article{BUMI_2003_8_6B_2_a10,
     author = {Balzano, M. and Durante, T.},
     title = {The $p${-Laplacian} in domains with small random holes},
     journal = {Bollettino della Unione matematica italiana},
     pages = {435--458},
     publisher = {mathdoc},
     volume = {Ser. 8, 6B},
     number = {2},
     year = {2003},
     zbl = {1177.35061},
     mrnumber = {MR1988215},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_2_a10/}
}
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Balzano, M.; Durante, T. The $p$-Laplacian in domains with small random holes. Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 2, pp. 435-458. http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_2_a10/