A sharp estimate a la Calderon-Zygmund for the p-Laplacian

Lorenzo Brasco (1, 2) , Filippo Santambrogio (3)

1 Department of Mathematics [Ferrara]
2 I2M - Institut de Mathématiques de Marseille
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We consider local weak solutions of the Poisson equation for the p−Laplace operator. We prove a higher differentiability result, under an essentially sharp condition on the right-hand side. The result comes with a local scaling invariant a priori estimate.

Mots clés: Degenerate quasilinear elliptic equations; regularity of solutions; higher differentiability

Domaines: Equations aux dérivées partielles [math.AP]

Lorenzo Brasco, Filippo Santambrogio. A sharp estimate a la Calderon-Zygmund for the p-Laplacian. Communications in Contemporary Mathematics, 2018, 20 (3), pp.1750030. ⟨10.1142/S0219199717500304⟩. ⟨hal-01347877⟩