Homogenization of multivalued monotone operators with variable growth exponent

Svetlana Pastukhova; Valeria Chiadò Piat

doi:10.3934/nhm.2020013

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2020, Volume 15, Issue 2: 281-305. Doi: 10.3934/nhm.2020013

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Homogenization of multivalued monotone operators with variable growth exponent

Svetlana Pastukhova^1, , and
Valeria Chiadò Piat^2,

1.
Russian Technological University, prospekt Vernadskogo 78, Moscow 119454, Russia
2.
Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

^* Corresponding author: Svetlana Pastukhova
^* Corresponding author: Svetlana Pastukhova

Received: February 28, 2019

Revised: March 31, 2020

Early access: May 2020

Published: June 2020

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Abstract

We consider the Dirichlet problem for an elliptic multivalued maximal monotone operator $ {\mathcal A}_\varepsilon $ satisfying growth estimates of power type with a variable exponent. This exponent $ p_\varepsilon(x) $ and also the symbol of the operator $ {\mathcal A}_\varepsilon $ oscillate with a small period $ \varepsilon $ with respect to the space variable $ x $. We prove a homogenization result for this problem.

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Mathematics Subject Classification: Primary: 35J60, 35J57; Secondary: 35J99.

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