Some class of nonlinear inequalities with gradient constraints in Orlicz spaces

Ajagjal, S.; Meskine, D.

doi:10.2478/mjpaa-2020-0022

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.

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Some class of nonlinear inequalities with gradient constraints in Orlicz spaces

Abstract

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