Characterization of the Critical Value for a Quasilinear Elliptic Equation with Arbitrary Growth with Respect to the Gradient

  • Fatima AqelEmail author
  • Nour Eddine Alaa


The aim of this work is to study a quasilinear elliptic equation where we are particularly interested in the characterization of the critical value, which appears as the Lagrange multiplier in the functional minimization associated with the dual problem, over one close convex subset of \(L^\infty \times (W^{1,\infty })^N\). We are going to give a generalization of Alaa (Etude d’équations elliptiques non linéaires à dépendance convexe en le gradient et à données mesures. Ph.D. Thesis, University of Nancy I, 1989) method in the case of an upper space dimension \((N\ge 2)\).


Critical value quasilinear equation functional minimization lower semicontinuity data measures 

Mathematics Subject Classification

26A15 26A51 35A01 35B09 58J10 35J62 



The authors are very thankful to the anonymous referee for his/her careful reading of the manuscript and valuable comments on this paper.


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Authors and Affiliations

  1. 1.University of Cadi Ayyad Faculty of Sciences and Techniques Laboratory of LAMAIMarrakechMorocco

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