Pseudo-monotonicity and degenerate elliptic operators of second order

Abstract

Extending the theory of pseudo-monotone mappings in weighted Sobolev spaces, we prove some existence results for degenerate or singular elliptic equations generated by the second-order differential operator $$ Au(x)=-mathop{m div}a(x,u,abla u))+a_0(x,u,abla u), $$ (in particular, when only large monotonicity is satisfied)

Keywords

• Weighted Sobolev spaces
• pseudo-monotonicity
• nonlinear degenerate elliptic operators.