Strongly nonlinear elliptic problem with measure data in Musielak-Orlicz spaces

Abstract

In this paper, we investigate the existence theorem of entropy solutions for nonlinear elliptic problem of the type −div⁡(a(x,u,∇u)+Φ(x,u))+g(x,u,∇u)=μ in Ω, in the setting of Musielak-Orlicz spaces. The lower order term Φ verifies the natural growth condition, the nonlinearity g has a natural growth with respect to its third argument and with sign condition, no Δ2-condition is assumed on the Musielak function, and the datum μ is assumed to belong to L1(Ω)+W−1Eφ¯(Ω).

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