Geodesic
Equivalence of entropy and renormalized solutions of the anisotropic elliptic problem in unbounded domains with measure data
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2020), pp. 30-45

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We consider a class of anisotropic elliptic equations of second order with variable exponents of nonlinearity when a special form of Radon measure is used as the right-hand side. In anisotropic Sobolev spaces with variable exponents of nonlinearity, the some properties and uniqueness of entropy and renormalized solutions of the Dirichlet problem in arbitrary domains are established. In addition, we prove the equivalence of entropy and renormalized solutions of the considered problem.
Mots-clés : anisotropic elliptic equation, existence of solution
Keywords: entropy solution, renormalized solution, uniqueness of solution, variable exponent, Radon measure data, Dirichlet problem, unbounded domain. 
@article{IVM_2020_1_a3,
     author = {L. M. Kozhevnikova},
     title = {Equivalence of entropy and renormalized solutions of the anisotropic elliptic problem in unbounded domains with measure data},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {30--45},
     publisher = {mathdoc},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_1_a3/}
}
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L. M. Kozhevnikova. Equivalence of entropy and renormalized solutions of the anisotropic elliptic problem in unbounded domains with measure data. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2020), pp. 30-45. http://geodesic.mathdoc.fr/item/IVM_2020_1_a3/