Geodesic
On entropy solutions of anisotropic elliptic equations with variable nonlinearity indices
Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 63 (2017) no. 3, pp. 475-493

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For a certain class of second-order anisotropic elliptic equations with variable nonlinearity indices and $L_1$ right-hand side we consider the Dirichlet problem in arbitrary unbounded domains. We prove the existence and uniqueness of entropy solutions in anisotropic Sobolev spaces with variable indices. 
@article{CMFD_2017_63_3_a5,
     author = {L. M. Kozhevnikova},
     title = {On entropy solutions of anisotropic elliptic equations with variable nonlinearity indices},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {475--493},
     publisher = {mathdoc},
     volume = {63},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2017_63_3_a5/}
}
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L. M. Kozhevnikova. On entropy solutions of anisotropic elliptic equations with variable nonlinearity indices. Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 63 (2017) no. 3, pp. 475-493. http://geodesic.mathdoc.fr/item/CMFD_2017_63_3_a5/