Nonlinear and non-coercive elliptic problems with integrable data

Mohsen Ben Cheikh Ali (1) , Olivier Guibé (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

In this paper we study existence and uniqueness of renormalized solution to the following problem $\lambda ( x,u) -div a( x,Du) +\Phi ( x,u)) =f$ with $f$ in $L^1$ and with Dirichlet-Neumann boundary condition. The main difficulty in this task is that in general the operator entering in the above equation is not coercive in a Sobolev space. Moreover, the possible degenerate character of $\lambda$ with respect to $u$ renders more complex the proof of uniqueness for integrable data $f$.

Mots clés: existence; uniqueness; non-coercive problems; integrable data

Domaines: Equations aux dérivées partielles [math.AP]

Mohsen Ben Cheikh Ali, Olivier Guibé. Nonlinear and non-coercive elliptic problems with integrable data. Advances in Mathematical Sciences and Applications, 2006, 16 (1), pp.275--297. ⟨hal-00263585⟩