Abstract:
A second-order quasilinear elliptic equation with a measure of special form on the right-hand side is considered. Restrictions on the structure of the equation are imposed in terms of a generalized NN-function such that the conjugate function obeys the Δ2Δ2-condition and the corresponding Musielak-Orlicz space is not necessarily reflexive. In an arbitrary domain satisfying the segment property, the existence of an entropy solution of the Dirichlet problem is proved. It is established that this solution is renormalized.
Bibliography: 29 titles.
Citation:
A. P. Kashnikova, L. M. Kozhevnikova, “Existence of solutions of nonlinear elliptic equations with measure data in Musielak-Orlicz spaces”, Sb. Math., 213:4 (2022), 476–511
\Bibitem{KasKoz22}
\by A.~P.~Kashnikova, L.~M.~Kozhevnikova
\paper Existence of solutions of nonlinear elliptic equations with measure data in Musielak-Orlicz spaces
\jour Sb. Math.
\yr 2022
\vol 213
\issue 4
\pages 476--511
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Linking options:
https://www.mathnet.ru/eng/sm9632
https://doi.org/10.1070/SM9632
https://www.mathnet.ru/eng/sm/v213/i4/p38
This publication is cited in the following 10 articles:
L. M. Kozhevnikova, “Existence of an entropic solution of a nonlinear elliptic problem in an unbounded domain”, Theoret. and Math. Phys., 218:1 (2024), 106–128
L. M. Kozhevnikova, “Suschestvovanie renormalizovannogo resheniya nelineinogo ellipticheskogo uravneniya s L1L1-dannymi v prostranstve Rn”, Funktsionalnye prostranstva. Differentsialnye operatory. Problemy
matematicheskogo obrazovaniya, SMFN, 70, no. 2, Rossiiskii universitet druzhby narodov, M., 2024, 278–299
L. M. Kozhevnikova, “Existence of a Renormalized Solution of a Quasilinear Elliptic
Equation without the Sign Condition
on the Lower-Order Term”, Diff Equat, 60:6 (2024), 729
L. M Kozhevnikova, “EXISTENCE OF A RENORMALIZED SOLUTION OF A QUASI-LINEAR ELLIPTIC EQUATION WITHOUT THE SIGN CONDITION ON THE LOWEST TERM”, Differencialʹnye uravneniâ, 60:6 (2024), 764
F. Kh. Mukminov, O. S. Stekhun, “Existence and uniqueness of solutions to outer Zaremba problem for elliptic equations with measure–valued potential”, Ufa Math. J., 16:4 (2024), 53–75
L. M. Kozhevnikova, “Existence of a Renormalized Solution to a Nonlinear Elliptic Equation with L1-Data in the Space ℝn”, J Math Sci, 2024
V. F Vildanova, “UNIQUENESS OF THE ENTROPY SOLUTION TO THE DIRICHLET PROBLEM FOR AN ELLIPTIC EQUATION WITH A MEASURE-VALUED POTENTIAL IN A HYPERBOLIC SPACE”, Differencialʹnye uravneniâ, 60:12 (2024), 1653
V. F. Vildanova, “Uniqueness of the Entropy Solution of the Dirichlet Problem for
an Elliptic Equation with a Measure-Valued Potential in a Hyperbolic Space”, Diff Equat, 60:12 (2024), 1708
M. Ya. Spiridonov, “On an estimate for of an elliptic problem the solution in a domain with an infinite boundary”, Math. Mon., 56 (2023), 42–53
V. F. Vil'danova, F. Kh. Mukminov, “Entropy solution for an equation with measure-valued potential in a hyperbolic space”, Sb. Math., 214:11 (2023), 1534–1559
Citation in format AMSBIB
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