A nonlinear degenerate elliptic problem with W^{1,1}_0 solutions

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

1 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]
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 unique W^{1,1}_0 distributional solution under suitable summability assumptions on the source in Lebesgue spaces. Moreover, we prove that our problem has no solution if the source is a Radon measure concentrated on a set of zero harmonic capacity.

Domaines: Equations aux dérivées partielles [math.AP]

Lucio Boccardo, Gisella Croce, Luigi Orsina. A nonlinear degenerate elliptic problem with W^{1,1}_0 solutions. Manuscripta mathematica, 2011. ⟨hal-00606417⟩