A Contribution to the Theory of Quasilinear Elliptic Equations and Application to the Minimization of Integral Functionals

The aim of this work is to study the existence of solutions of quasilinear elliptic problems of the type {-div([a(x) + vertical bar u vertical bar(q)]del u) + b(x) u vertical bar u vertical bar(p-1) vertical bar del u vertical bar(2) = f(x), in Omega; u = 0, on partial derivative Omega. Then we study the minimization of integral functional of the type J(v) = 1 2 integral(Omega) [a(x)+vertical bar v vertical bar(r)]vertical bar del v vertical bar(2) -integral(Omega) fv, (0, 1) with f is an element of L(m)(Omega). Since we can have m < 2N/N+2, the study of minimization with nonregular data f (i.e. f is not an element of W(-1,2)(Omega)) will be possible.