Geodesic
Existence and uniqueness of solutions to outer Zaremba problem for elliptic equations with measure–valued potential
Ufa mathematical journal, Tome 16 (2024) no. 4, pp. 53-75 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the exterior of a ball in the space $\mathbb{R}^n$ we consider the Zaremba and Neumann problems for quasilinear second order elliptic problems with a measure–valued potential. We proved the existence and uniqueness of entropy solution to the Zaremba and Neumann problems.
Keywords: nonlinear elliptic equation, entropy solution, Radon measure, Zaremba problem. 
@article{UFA_2024_16_4_a4,
     author = {F. Kh. Mukminov and O. S. Stekhun},
     title = {Existence and uniqueness of solutions to outer {Zaremba} problem for elliptic equations with measure{\textendash}valued potential},
     journal = {Ufa mathematical journal},
     pages = {53--75},
     year = {2024},
     volume = {16},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2024_16_4_a4/}
}
TY  - JOUR
AU  - F. Kh. Mukminov
AU  - O. S. Stekhun
TI  - Existence and uniqueness of solutions to outer Zaremba problem for elliptic equations with measure–valued potential
JO  - Ufa mathematical journal
PY  - 2024
SP  - 53
EP  - 75
VL  - 16
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/UFA_2024_16_4_a4/
LA  - en
ID  - UFA_2024_16_4_a4
ER  - 
%0 Journal Article
%A F. Kh. Mukminov
%A O. S. Stekhun
%T Existence and uniqueness of solutions to outer Zaremba problem for elliptic equations with measure–valued potential
%J Ufa mathematical journal
%D 2024
%P 53-75
%V 16
%N 4
%U http://geodesic.mathdoc.fr/item/UFA_2024_16_4_a4/
%G en
%F UFA_2024_16_4_a4
F. Kh. Mukminov; O. S. Stekhun. Existence and uniqueness of solutions to outer Zaremba problem for elliptic equations with measure–valued potential. Ufa mathematical journal, Tome 16 (2024) no. 4, pp. 53-75. http://geodesic.mathdoc.fr/item/UFA_2024_16_4_a4/

[1] Ph. Benilan, L. Boccardo, Th. Gallouët, R. Gariepy, M. Pierre, J.L. Vazquez, “An $L^1$–theory of existence and nuniqueness of solutions of nonlinear elliptic equation”, Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV, 22:2 (1995), 241–273 | MR | Zbl

[2] N. Saintier, L. Véron, “Nonlinear elliptic equations with measure valued absorption potential”, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5), 22:1 (2021), 351–397 | MR | Zbl

[3] A. Malusa, M.M. Porzio, “Renormalized solutions to elliptic equations with measure data in unbounded domains”, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods, 67 (2007), 2370–2389 | DOI | MR | Zbl

[4] L.M. Kozhevnikova, A.P. Kashnikova, “Equivalence of entropy and renormalized solutions of a nonlinear elliptic problem in Musielak — Orlicz spaces”, Differ. Equ, 59:1 (2023), 34–50 | DOI | DOI | MR | MR | Zbl

[5] L.M. Kozhevnikova, “Existence of an entropic solution of a nonlinear elliptic problem in an unbounded domain”, Theor. Math. Phys, 218:1 (2024), 106–128 | DOI | DOI | MR | Zbl

[6] S. Ouaro, N. Sawadogo, “Nonlinear elliptic $p(u)$–Laplacian problem with Fourier boundary condition”, Cubo, 22:1 (2020), 85–124 | DOI | MR | Zbl

[7] V.F. Vil'danova, F.Kh. Mukminov, “Entropy solution for equation with a measure valued potential in hyperbolic space”, Sb. Math., 214:11 (2023), 1534–1559 | DOI | DOI | MR | Zbl

[8] F. Crispo, P. Maremonti, “An interpolation inequality in exterior domains”, Rend. Semin. Mat. Univ. Padova, 112 (2004), 11–39 | MR | Zbl

[9] 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 | DOI | DOI | MR | Zbl

[10] M.B. Benboubker, E. Azroul, A. Barbara, “Quasilinear elliptic problems with nonstandard growth”, Electron. J. Differ. Equ, 2011 (2011), 62 | DOI | MR | Zbl

[11] N. Dunford, J.T. Schwartz, Linear operators, v. I, General theory, Interscience Publishers, New York, 1958 | MR | Zbl

[12] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Gauthier–Villars, Dunod, Paris, 1969 | MR