Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-18T21:30:26.221Z Has data issue: false hasContentIssue false
  • English
  • Français

Stochastic reinforcement problems and ergodic theory

Published online by Cambridge University Press:  14 November 2011

M. Balzano  and
G. Paderni
M. Balzano
Affiliation:
Universitá degli Studi di Cassino, Dipartimento di Ingegneria Industriale, Via Zamosch, 43, 03043 Cassino (FR), Italy
G. Paderni
Affiliation:
Universitá degli Studi di Cassino, Dipartimento di Ingegneria Industriale, Via Zamosch, 43, 03043 Cassino (FR), Italy
Get access Rights & Permissions [Opens in a new window]

Synopsis

We study the asymptotic behaviour of Dirichlet problems in domains of R2 bounded by thin layers whose thickness is given by means of an assigned ergodic random function. Using a capacitary method together with ergodic theorems for additive and superadditive processes, we are able to characterise the limit problem precisely.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 121 , Issue 1-2 , 1992 , pp. 33 - 53
Copyright
Copyright © Royal Society of Edinburgh 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Acerbi, E. and Buttazzo, G.. Reinforcement problems in the calculus of variations. Ann. Inst. H. Poincaré, Anal. Non Linéaire 4 (1986), 273–284.CrossRefGoogle Scholar
2Akcoglu, M. A. and Krengel, U.. Ergodic theorems for superadditive processes. J. Reine Angew. Math. 323 (1981), 53–67.Google Scholar
3Balzano, M. and Paderni, G.. Dirichlet problems in domains bounded by thin layers with random thickness. J. Math. Pures Appl. 69 (1990), 335–367.Google Scholar
4Brezis, H., Caffarelli, L. A. and Friedman, A.. Reinforcement problems for elliptic equations and variational inequalities. Ann. Mat. Pura Appl. 123 (1980), 219–246.CrossRefGoogle Scholar
5Buttazzo, G., Maso, G. Dal and Mosco, U.. Asymptotic behaviour for Dirichlet problems in domains bounded by thin layers. In Partial Differential Equations and Calculus of Variations, Essays in honor of E. De Giorgi, 193–249 (Boston: Birkhauser, 1989).Google Scholar
6Buttazzo, G. and Kohn, R. V.. Reinforcement by a thin layer with oscillating thickness. Appl. Math. Optim. 16 (1987) 247–261.CrossRefGoogle Scholar
7Caffarelli, L. A. and Friedman, A.. Reinforcement problems in elasto-plasticity. Rocky Mountain J. Math. 10 (1980), 155–184.CrossRefGoogle Scholar
8Maso, G. Dal and Modica, L.. Nonlinear stochastic homogenization and ergodic theory. J. Reine Angew. Math. 368 (1986), 27–42.Google Scholar
9Kingman, J. F. C.. Subadditive ergodic theory. Ann. Prob. 6 (1973), 833–909.Google Scholar
10Wiener, N.. The ergodic theorem. Duke Math. J. 5 (1939), 1–18.CrossRefGoogle Scholar