We would like to present some new results regarding the existence of a minimal solution to some variational inequalities of the type
where Ω is a domain in ℝn, K is a closed convex subset of W01,p(Ω), A is a nonlinear operator defined from W01,p(Ω) into its dual by
for all v∈W01,p(Ω) and f∈Lq(Ω) where q is the conjugate of p.
This is joint work with S. Guesmia and S. Harkat.