Strongly nonlinear degenerated elliptic unilateral problems via convergence of truncations

Abstract

We prove an existence theorem for a strongly nonlinear degenerated elliptic inequalities involving nonlinear operators of the form $Au+g(x,u,abla u)$. Here $A$ is a Leray-Lions operator, $g(x,s,xi)$ is a lower order term satisfying some natural growth with respect to $|abla u|$. There is no growth restrictions with respect to $|u|$, only a sign condition. Under the assumption that the second term belongs to $W^{-1,p'}(Omega,w^*)$, we obtain the main result via strong convergence of truncations.

Keywords

• Weighted Sobolev spaces
• Hardy inequality
• variational ineqality
• strongly nonlinear degenerated elliptic operators
• truncations.