Full paper in PDF:
$%P. Lindqvist and J. Manfredi, Note on  oo  -superharmonic functions, Rev. Mat. Univ. Complut. Madrid 10 (1997), no. 1, 472–480.%$

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.