Geodesic
Entropy and renormalized solutions for a nonlinear elliptic problem in Musielak--Orlicz spaces
Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 1, pp. 98-115

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In this paper, we establish the equivalence of entropy and renormalized solutions of second-order elliptic equations with nonlinearities defined by the Musielak–Orlicz functions and the right-hand side from the space $L_1(\Omega).$ In nonreflexive Musielak—Orlicz—Sobolev spaces, we prove the existence and uniqueness of both entropy and renormalized solutions of the Dirichlet problem in domains with a Lipschitz boundary.
Keywords: second-order elliptic equation, entropy solution, renormalized solution, Musielak–Orlicz–Sobolev space, existence and uniqueness of solutions. 
@article{CMFD_2023_69_1_a6,
     author = {L. M. Kozhevnikova},
     title = {Entropy and renormalized solutions for a nonlinear elliptic problem in {Musielak--Orlicz} spaces},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {98--115},
     publisher = {mathdoc},
     volume = {69},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2023_69_1_a6/}
}
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L. M. Kozhevnikova. Entropy and renormalized solutions for a nonlinear elliptic problem in Musielak--Orlicz spaces. Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 1, pp. 98-115. http://geodesic.mathdoc.fr/item/CMFD_2023_69_1_a6/