LAUSR

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’equations elliptiques non lineaires a dependance convexe en le gradient et a donnees mesures. Ph.D. Thesis, University of Nancy I, 1989) method in the case of an upper space dimension $$(N\ge 2)$$.