Full paper in PDF:
$%P. Lindqvist and J. Manfredi, Note on  oo  -superharmonic functions, Rev. Mat. Univ. Complut. Madrid 10 (1997), no. 1, 472480.%$

Note on  oo  -Superharmonic Functions
Peter LINDQVIST and Juan MANFREDI
Department of Mathematics
The University of Texas at Austin
Austin, TX 78712 USA
Department of Mathematics
University of Pittsburgh
Pittsburgh, PA 15260 USA

ABSTRACT

The purpose of this note is to show that all viscosity supersolutions of

       sum  @v  @n @2xi
D oo n  =_   @xi@xj@xi@xj < 0

are variational. That is, they are limits of p  -superharmonic functions, induced by the operator

Dpn = div(| \~/ n |p-2 \~/ n,

as p  approaches  oo  . In addition, it is shown that each viscosity supersolution of D oo n < 0  is Lipschitz continuous.

1991 Mathematics Subject Classification: 35J70, 26A16.