The p -Laplacian in domains with small random holes

M. Balzano; T. Durante

Bollettino dell'Unione Matematica Italiana (2003)

  • Volume: 6-B, Issue: 2, page 435-458
  • ISSN: 0392-4041

Abstract

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P h {ll -div (|Duh|p-2 Duh)=g, & in D Eh uhH1,p0(D Eh). . where 2 ≤ p ≤ n and E h are random subsets of a bounded open set D of R n n ≥ 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.

How to cite

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Balzano, M., and Durante, T.. "The $p$-Laplacian in domains with small random holes." Bollettino dell'Unione Matematica Italiana 6-B.2 (2003): 435-458. <http://eudml.org/doc/195896>.

@article{Balzano2003,
abstract = {$P_h$\{ll -div (|Duh|p-2 Duh)=g, & in D Eh uhH1,p0(D Eh). . 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.},
author = {Balzano, M., Durante, T.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {435-458},
publisher = {Unione Matematica Italiana},
title = {The $p$-Laplacian in domains with small random holes},
url = {http://eudml.org/doc/195896},
volume = {6-B},
year = {2003},
}

TY - JOUR
AU - Balzano, M.
AU - Durante, T.
TI - The $p$-Laplacian in domains with small random holes
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/6//
PB - Unione Matematica Italiana
VL - 6-B
IS - 2
SP - 435
EP - 458
AB - $P_h${ll -div (|Duh|p-2 Duh)=g, & in D Eh uhH1,p0(D Eh). . 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.
LA - eng
UR - http://eudml.org/doc/195896
ER -

References

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  11. OZAWA, S., Random media and the eigenvalues of the Laplacian, Comm. Math. Phys., 94 (1984), 421-437. Zbl0555.35101MR763745
  12. PAPANICOLAOU, G. C.- VARADHAN, S. R. S., Diffusion in regions with many small holes, Stochastic Differential Systems, Filtering and Control. Proc. of the IFIPWG 7/1 Working Conference (Vilnius, Lithuania, 1978), 190-206. Lectures Notes in Control and Information Sci., 25, Springer-Verlag, Berlin (1980). Zbl0485.60076MR609184
  13. ZIEMER, W. P., Weakly Differentiable Functions, Springer-Verlag, 1989. Zbl0692.46022MR1014685

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