Existence of solutions for some noncercive elliptic problems involving derivatives of nonlinear terms

Lucio Boccardo (1) , Gisella Croce (2) , Luigi Orsina (1)

1 Dipartimento di Matematica Guido Castelnuovo
2 LMAH - Laboratoire de Mathématiques Appliquées du Havre

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.

Domaines: Equations aux dérivées partielles [math.AP]

Lucio Boccardo, Gisella Croce, Luigi Orsina. Existence of solutions for some noncercive elliptic problems involving derivatives of nonlinear terms. Differential equations and applications, pp.3-9, 2012. ⟨hal-00708549⟩