A note on bounds for non-linear multivalued homogenized operators
type: Item
instance of: scholarly article
title: A note on bounds for non-linear multivalued homogenized operators
zbMATH Open document ID: 0940.47041
DOI: 10.1023/A:1023210332327
published in: Applications of Mathematics
publication date: 2000-05-22T00:00:00Z
full work available at URL: https://eudml.org/doc/32998
review text: The paper deals with the homogenization problem for equations with nonlinear maximal monotone multivalued operators of the type \[ - \text{div}\left (a\left ({x\over \varepsilon}, Du_\varepsilon \right)\right) \ni f \quad \text{in } \Omega, \] that appear in nonlinear elasticity and plasticity. Since the computation of homogenized operators is difficult, their bounds and estimates are useful. The author generalizes estimates of Reuss-Voigt-Wiener and Hahin-Shtrikman type to nonlinear monotone operators of potential type mentioned above. The proof is based on a variational principle using means of convex analysis, namely duality mapping and Yosida approximation.
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 1450142
zbMATH Keywords: multivalued operators
zbMATH Keywords: maximal monotone operators
zbMATH Keywords: homogenization
zbMATH Keywords: Reuss-Voigt-Wiener bounds
zbMATH Keywords: Hashin-Shtrikman bounds
author: Nils Svanstedt
MaRDI profile type: Publication
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OpenAlex ID: W1504028153
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description: scientific article; zbMATH DE number 1450142