Existence Results for Some Nonuniformly Elliptic Equations with Irregular Data

In this paper we prove the existence of solutions of some nonlinear elliptic equations with degenerate coercivity of the type ½ divŽ Du Ž1 u . . divŽ F., in , u 0, on , when the datum F belongs to the space LrŽ ., where r 2 and Ž0, 1..