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Mathematics Research Report MRR95-034
On The Existence Of Lipschitz Barriers For Quasilinear Elliptic Equations
Timothy R. Cranny
Abstract:
It is well-known that quasilinear elliptic PDE's permit the exitence of
Lipschitz
barriers for arbitrary Dirichlet boundary data only under certain
restrictions upon the
behaviour of the differential operator for large gradient. We present here
a simple
proof that a sufficiently tight bound on the supremum norm of solutions
ensures the
existence of Lipschitz barriers even when these restrictions are
substantially weakened.
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