Full paper in PDF:
$%L. Esposito and G. Mingione, Some remarks on the regularity of weak solutions of degenerate elliptic systems, Rev. Mat. Complut. 11 (1998), no. 1, 203–219. %$

Some Remarks on the Regularity of Weak Solutions of Degenerate Elliptic Systems
Luca ESPOSITO and Giuseppe MINGIONE
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”
Università di Napoli “Federico II”
Complesso Monte S. Angelo
Via Cintia
80126 Napoli — Italy

Received: July 3, 1996
Revised: November 4, 1996
ABSTRACT

We prove the existence of second derivatives of the weak solutions u (- W 1,p of the degenerate system divA(Du) = 0 , where no differentiability is supposed on the monotone vector field nN nN A:R --> R . We also give a boundedness result for the scalar case.

1991 Mathematics Subject Classification: 35J60, 35D10.