Bulletin of the Australian Mathematical Society

Research Article

Pseudo-monotonicity and degenerated or singular elliptic operators

P. Drábeka1, A. Kufnera2 and V. Mustonena3

a1 Department of Mathematics, University of West Bohemia, Univerzitní 8, 306 14 Plzen˘, Czech Republic

a2 Mathematical Institute, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic

a3 Department of Mathematical Sciences, University of Oulu, Linnanmaa, 90570 Oulu, Finland

Abstract

Using the compactness of an imbedding for weighted Sobolev spaces (that is, a Hardy-type inequality), it is shown how the assumption of monotonicity can be weakened still guaranteeing the pseudo-monotonicity of certain nonlinear degenerated or singular elliptic differential operators. The result extends analogous assertions for elliptic operators.

(Received January 27 1998)