# Existence of solutions of degenerated unilateral problems with ${L}^{1}$ data

Lahsen Aharouch^{[1]}; Youssef Akdim^{[1]}

- [1] Faculté des Sciences Dhar-Mahraz Dép. de Math. et Informatique B.P 1796 Atlas Fès. Fès MAROC

Annales mathématiques Blaise Pascal (2004)

- Volume: 11, Issue: 1, page 47-66
- ISSN: 1259-1734

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topAharouch, Lahsen, and Akdim, Youssef. "Existence of solutions of degenerated unilateral problems with $L^1$ data." Annales mathématiques Blaise Pascal 11.1 (2004): 47-66. <http://eudml.org/doc/10499>.

@article{Aharouch2004,

abstract = {In this paper, we shall be concerned with the existence result of the Degenerated unilateral problem associated to the equation of the type $Au + g(x, u, \nabla u) = f - \{\rm div \}F,$ where $A$ is a Leray-Lions operator and $g$ is a Carathéodory function having natural growth with respect to $|\nabla u|$ and satisfying the sign condition. The second term is such that, $f\in L^1(\Omega )$ and $ F\in \Pi _\{i=1\}^N L^\{p^\{\prime\}\}(\Omega , w_i^\{1-p^\{\prime\}\})$.},

affiliation = {Faculté des Sciences Dhar-Mahraz Dép. de Math. et Informatique B.P 1796 Atlas Fès. Fès MAROC; Faculté des Sciences Dhar-Mahraz Dép. de Math. et Informatique B.P 1796 Atlas Fès. Fès MAROC},

author = {Aharouch, Lahsen, Akdim, Youssef},

journal = {Annales mathématiques Blaise Pascal},

language = {eng},

month = {1},

number = {1},

pages = {47-66},

publisher = {Annales mathématiques Blaise Pascal},

title = {Existence of solutions of degenerated unilateral problems with $L^1$ data},

url = {http://eudml.org/doc/10499},

volume = {11},

year = {2004},

}

TY - JOUR

AU - Aharouch, Lahsen

AU - Akdim, Youssef

TI - Existence of solutions of degenerated unilateral problems with $L^1$ data

JO - Annales mathématiques Blaise Pascal

DA - 2004/1//

PB - Annales mathématiques Blaise Pascal

VL - 11

IS - 1

SP - 47

EP - 66

AB - In this paper, we shall be concerned with the existence result of the Degenerated unilateral problem associated to the equation of the type $Au + g(x, u, \nabla u) = f - {\rm div }F,$ where $A$ is a Leray-Lions operator and $g$ is a Carathéodory function having natural growth with respect to $|\nabla u|$ and satisfying the sign condition. The second term is such that, $f\in L^1(\Omega )$ and $ F\in \Pi _{i=1}^N L^{p^{\prime}}(\Omega , w_i^{1-p^{\prime}})$.

LA - eng

UR - http://eudml.org/doc/10499

ER -

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