Entropy solutions of some nonlinear elliptic problems with measure data in Musielak-Orlicz spaces

Abstract

In this work, we prove an existence theorem of entropy solutions for nonlinear elliptic problem of the type − div(a(x, u, ∇u) + Φ(x, u)) = µ in Ω, in the setting of Musielak-Orlicz spaces. The lower order term Φ verifies the natural growth condition, no ∆2-condition is assumed on the Musielak function, and the datum µ is assumed to belong to L1(Ω) + W−1Eψ(Ω).

Keywords

• musielak-orlicz-sobolev spaces
• elliptic equation
• entropy solutions
• truncations