Rendiconti di Matematica e delle sue Applicazioni
ISSN 1120-7183 (print)
ISSN 2532-3350 (online)
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Entropy solutions of some nonlinear elliptic problems with measure data in Musielak-Orlicz spaces
Rachid Bouzyani, Badr El Haji, Mostafa El Moumni

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 Δ2-condition is assumed on the Musielak function, and the datum μ is assumed to belong to L1(Ω)+W-1Eψ(Ω)

Rend. Mat. Appl. (7) 43 (2022) 1-22; pdf file pdf