Some class of nonlinear inequalities with gradient constraints in Orlicz spaces

Abstract

In the present paper, we show the existence of solutions of some nonlinear inequalities of the form 〈Au + g(x, u,∇ u), v −u〉 ≥〈 f, v −u〉 with gradient constraint that depend on the solution itself, where A is a Leray-Lions operator defined on Orlicz spaces, g is a nonlinearity and f ∈ L1.

Keywords

• nonlinear variational inequalities
• nonlinear elliptic equations
• p-laplacian
• orlicz spaces
• 35j87
• 35j60
• 35j92
• 46e30