Geodesic
Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents
Sbornik. Mathematics, Tome 210 (2019) no. 3, pp. 417-446

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The Dirichlet problem is considered in arbitrary domains for a class of second-order anisotropic elliptic equations with variable nonlinearity exponents and right-hand sides in $L_1$. It is proved that an entropy solution exists in anisotropic Sobolev spaces with variable exponent. It is proved that the entropy solution obtained is a renormalized solution of the problem under consideration. Bibliography: 37 titles.
Keywords: entropy solution, renormalized solution, variable exponent, Dirichlet problem.
Mots-clés : anisotropic elliptic equation, existence of a solution 
@article{SM_2019_210_3_a3,
     author = {L. M. Kozhevnikova},
     title = {Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents},
     journal = {Sbornik. Mathematics},
     pages = {417--446},
     publisher = {mathdoc},
     volume = {210},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2019_210_3_a3/}
}
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L. M. Kozhevnikova. Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents. Sbornik. Mathematics, Tome 210 (2019) no. 3, pp. 417-446. http://geodesic.mathdoc.fr/item/SM_2019_210_3_a3/