UNIQUENESS OF THE ENTROPY SOLUTION TO THE DIRICHLET PROBLEM FOR AN ELLIPTIC EQUATION WITH A MEASURE-VALUED POTENTIAL IN A HYPERBOLIC SPACE

Мұқаба

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Тек жазылушылар үшін

Аннотация

We consider the Dirichlet problem in the hyperbolic space for a nonlinear equation of the second order with measure-valued potential. The assumptions on the structure of the equation are stated in terms of a generalized

Негізгі сөздер

Авторлар туралы

V. Vildanova

Institute of Mathematics with Computing Centre of Ufa Scientific Center of RAS

Email: gilvenera@mail.ru
Russia

Әдебиет тізімі

  1. Вильданова, В.Ф. Энтропийное решение для уравнения с мерозначным потенциалом в гиперболическом пространстве / В.Ф. Вильданова, Ф.Х. Мукминов // Мат. сб. — 2023. — Т. 214, № 11. — С. 37–62.
  2. Vil’danova, V.F. and Mukminov, F.Kh., Entropy solution for an equation with measure-valued potential in a hyperbolic space, Sb. Math., 2023, vol. 214, no. 11, pp. 1534–1559.
  3. An
  4. Кожевникова, Л.М. Эквивалентность энтропийных и ренормализованных решений нелинейной эллиптической задачи в пространствах Музилака–Орлича / Л.М. Кожевникова, А.П. Кашникова // Дифференц. уравнения. — 2023. — Т. 59, № 1. — С. 35–51.
  5. Kozhevnikova, L.M. and Kashnikova, A.P., Equivalence of entropy and renormalized solutions of a nonlinear elliptic problem in Musielak–Orlicz spaces, Differ. Equat., 2023, vol. 59, no. 1, pp. 34–50.
  6. Saintier, N. Nonlinear elliptic equations with measure valued absorption potential / N. Saintier, L. V’eron // Ann. Scuola Norm. Sup. Pisa Cl. Sci. — 2021. — V. 22, № 1. — P. 351–397.
  7. Malusa, A. Renormalized solutions to elliptic equations with measure data in unbounded domains / A. Malusa, M.M. Porzio // Nonlin. Anal. — 2007. — V. 67, № 8. — P. 2370–2389.
  8. Кашникова, А.П. Существование решений нелинейных эллиптических уравнений с данными в виде меры в пространствах Музилака–Орлича / А.П. Кашникова, Л.М. Кожевникова // Мат. сб. — 2022. — Т. 213, № 4. — С. 38–73.
  9. Kashnikova, A.P. and Kozhevnikova L.M., Existence of solutions of nonlinear elliptic equations with measure data in Musielak–Orlicz spaces, Sb. Math., 2022, vol. 213, no. 4, pp. 476–511.
  10. Vildanova, V.F. Perturbations of nonlinear elliptic operators by potentials in the space of multiplicators / V.F. Vildanova, F.Kh. Mukminov // J. Math. Sci. — 2021. — V. 257, № 5. — P. 569–578.
  11. Chlebicka, I. Measure data elliptic problems with generalized Orlicz growth / I. Chlebicka // Proc. Roy. Soc. Edinburgh. Sect. A. — 2023. — V. 153, № 2. — P. 588–618.
  12. Chlebicka, I. Essentially fully anisotropic Orlicz functions and uniqueness to measure data problem / I. Chlebicka, P. Nayar // Math. Methods Appl. Sci. — 2022. — V. 45, № 14. — P. 8503–8527.
  13. Musielak, J. Orlicz Spaces and Modular Spaces / J. Musielak. — Berlin : Springer-Verlag, 1983. — 222 p.
  14. Harjulehto, P. Orlicz Spaces and Generalized Orlicz Spaces / P. Harjulehto, P. H‥ast‥o. — Cham : Springer, 2019. — 167 p.
  15. Aubin, T. Nonlinear Analysis on Manifolds. Monge–Amp`ere Equations / T. Aubin. — New York : Springer-Verlag, 1982. — 204 p.
  16. Renormalized solutions of nonlinear elliptic problems in generalized Orlicz spaces / P. Gwiazda, P. Wittbold, A. Wroblewska, A. Zimmermann // J. Differ. Equat. — 2012. — V. 253, № 2. — P. 635–666.
  17. Колмогоров, А.Н. Элементы теории функций и функционального анализа / А.Н. Колмогоров, С.В. Фомин. — М. : Наука, 1976. — 543 с.
  18. Kolmogorov, A.N. and Fomin, S.V., Elements of the Theory of Functions and Functional Analysis, Metric and Normed Spaces, Graylock Press, 1957.

Қосымша файлдар

Қосымша файлдар
Әрекет
1. JATS XML
Жүктеу

© Russian Academy of Sciences, 2024