OBSTACLE PROBLEMS FOR DEGENERATE ELLIPTIC EQUATIONS WITH NONHOMOGENEOUS NONLINEAR BOUNDARY CONDITIONS

In this paper we study the questions of existence and uniqueness of solutions for equations of type -div a(x, Du)+ gamma(u) phi, posed in an open bounded subset. of RN, with nonlinear boundary conditions of the form a(x, Du) . eta + beta(u) psi. The nonlinear elliptic operator div a( x, Du) modeled on the p-Laplacian operator Delta(p)(u) = div(vertical bar Du vertical bar(p- 2) Du), with p > 1, gamma and beta maximal monotone graphs in R(2) such that 0 epsilon gamma(0) boolean AND beta(0), R not equal <(D(gamma))over bar> subset of D(beta) and the data phi epsilon L(1)(Omega) and psi epsilon L(1)(partial derivative Omega). Since D(gamma) not equal R, we are dealing with obstacle problems. For this kind of problems the existence of weak solution, in the usual sense, fails to be true for nonhomogeneous boundary conditions, so a new concept of solution has to be introduced.