Volume 48, Issue 4
Existence of Renormalized Solutions of Nonlinear Elliptic Problems in Weighted Variable-Exponent Space

Youssef Akdim & Chakir Allalou

J. Math. Study, 48 (2015), pp. 375-397.

Published online: 2015-12

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  • Abstract

In this article, we study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion $β(u)-div(a(x,Du)+F(u)) ∋ f$ in $Ω$  where $f ∈ L^1(Ω).$ A vector field $a(.,.)$ is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in the framework of weighted variable exponent Sobolev spaces, we prove existence of renormalized solutions for general $L^1$-data.

  • AMS Subject Headings

35J15, 35J70, 35J85

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

akdimyoussef@yahoo.fr (Youssef Akdim)

chakir_alalou@yahoo.fr (Chakir Allalou)

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  • RIS
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@Article{JMS-48-375, author = {Akdim , Youssef and Allalou , Chakir}, title = {Existence of Renormalized Solutions of Nonlinear Elliptic Problems in Weighted Variable-Exponent Space}, journal = {Journal of Mathematical Study}, year = {2015}, volume = {48}, number = {4}, pages = {375--397}, abstract = {

In this article, we study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion $β(u)-div(a(x,Du)+F(u)) ∋ f$ in $Ω$  where $f ∈ L^1(Ω).$ A vector field $a(.,.)$ is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in the framework of weighted variable exponent Sobolev spaces, we prove existence of renormalized solutions for general $L^1$-data.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v48n4.15.05}, url = {http://global-sci.org/intro/article_detail/jms/9943.html} }
TY - JOUR T1 - Existence of Renormalized Solutions of Nonlinear Elliptic Problems in Weighted Variable-Exponent Space AU - Akdim , Youssef AU - Allalou , Chakir JO - Journal of Mathematical Study VL - 4 SP - 375 EP - 397 PY - 2015 DA - 2015/12 SN - 48 DO - http://doi.org/10.4208/jms.v48n4.15.05 UR - https://global-sci.org/intro/article_detail/jms/9943.html KW - Weighted variable exponent Sobolev spaces, truncations, Young's Inequality, elliptic operators. AB -

In this article, we study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion $β(u)-div(a(x,Du)+F(u)) ∋ f$ in $Ω$  where $f ∈ L^1(Ω).$ A vector field $a(.,.)$ is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in the framework of weighted variable exponent Sobolev spaces, we prove existence of renormalized solutions for general $L^1$-data.

Akdim , Youssef and Allalou , Chakir. (2015). Existence of Renormalized Solutions of Nonlinear Elliptic Problems in Weighted Variable-Exponent Space. Journal of Mathematical Study. 48 (4). 375-397. doi:10.4208/jms.v48n4.15.05
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