| Abstract: | We consider the problem of finding a solution to a class of nonlinear elliptic variational inequalities. These inequalities may be defined on bounded or unbounded domains Ω, and the nonlinearity can depend on gradient terms. Appropriate definitions of sub-and supersolutions relative to the constraint sets are given. By using a mixture of maximal monotone operator theory and compactness arguments we prove the existence of a H2(Ω) solution lying between a given subsolution φ1 and a given supersolution φ2≧φ1, when Ω is bounded, and a H1(Ω) solution when Ω is unbounded. |
