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

作者：Boccardo Lucio^*

来源：Milan Journal of Mathematics, 2011, 79(1): 193-206.

DOI：10.1007/s00032-011-0150-y

• Quasilinear elliptic equations
• quadratic growth
• 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.

• 出版日期2011-6