Geodesic
Existence of an entropic solution of a nonlinear elliptic problem in an unbounded domain
Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 1, pp. 124-148

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We consider a second-order quasilinear elliptic equation with an integrable right-hand side. We formulate constraints on the structure of the equation in terms of a generalized $N$-function. We prove the existence of an entropic solution of the Dirichlet problem in nonreflexive Musielak–Orlicz–Sobolev spaces in an arbitrary unbounded strictly Lipschitz domain.
Keywords: quasilinear elliptic equation, unbounded domain, Musielak–Orlicz space.
Mots-clés : entropic solution, existence of solution 
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     author = {L. M. Kozhevnikova},
     title = {Existence of an entropic solution of a nonlinear elliptic problem in an unbounded domain},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {124--148},
     publisher = {mathdoc},
     volume = {218},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2024_218_1_a7/}
}
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L. M. Kozhevnikova. Existence of an entropic solution of a nonlinear elliptic problem in an unbounded domain. Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 1, pp. 124-148. http://geodesic.mathdoc.fr/item/TMF_2024_218_1_a7/