Existence of solutions for some noncercive elliptic problems involving   derivatives of nonlinear terms
  We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a W^{1,1}_0 solution which is distributional or entropic, according to the growth assumptions on a lower order term in divergence form. 
Lucio Boccardo, Gisella Croce (LMAH), Luigi Orsina
math.AP