On some nonlinear nonhomogeneous elliptic unilateral problems involving noncontrollable lower order terms with measure right hand side

Volume 40 / 2013

C. Yazough, E. Azroul, H. Redwane Applicationes Mathematicae 40 (2013), 197-219 MSC: Primary 47A15; Secondary 46A32, 47D20. DOI: 10.4064/am40-2-4

Abstract

We prove the existence of entropy solutions to unilateral problems associated to equations of the type $Au-\mathop{\rm div}(\phi (u))=\mu \in L^{1}(\varOmega )+W^{-1,p'(\cdot )}(\varOmega )$, where $A$ is a Leray–Lions operator acting from $W_{0}^{1,p(\cdot )}(\varOmega )$ into its dual $W^{-1,p(\cdot )}(\varOmega )$ and $\phi \in C^{0}(\mathbb R,\mathbb R^{N})$.

Authors

  • C. YazoughDepartment of Mathematics
    Faculty of Sciences Dhar El Mahraz
    University of Fez
    Laboratory LAMA
    B.P. 1796 Atlas Fez, Morocco
    e-mail
  • E. AzroulFaculty of Sciences Dhar El Mahraz
    University of Fez
    Laboratory LAMA
    Department of Mathematics
    B.P. 1796 Atlas Fez, Morocco
    e-mail
  • H. RedwaneFaculté des Sciences Juridiques,
    Économiques et Sociales
    Université Hassan 1
    B.P. 784, Settat, Morocco
    e-mail

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