Integrability of Solutions of Nonlinear Elliptic Equations with Right-Hand Sides from Logarithmic Classes
Matematičeskie zametki, Tome 74 (2003) no. 5, pp. 676-685.

Voir la notice de l'article provenant de la source Math-Net.Ru

We establish the existence of a weak solution to the Dirichlet problem belonging to a Sobolev space for nonlinear elliptic equations of second order with right-hand sides from a wide class of functions defined in terms of the logarithmic function.
@article{MZM_2003_74_5_a3,
     author = {A. A. Kovalevsky},
     title = {Integrability of {Solutions} of {Nonlinear} {Elliptic} {Equations} with {Right-Hand} {Sides} from {Logarithmic} {Classes}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {676--685},
     publisher = {mathdoc},
     volume = {74},
     number = {5},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_5_a3/}
}
TY  - JOUR
AU  - A. A. Kovalevsky
TI  - Integrability of Solutions of Nonlinear Elliptic Equations with Right-Hand Sides from Logarithmic Classes
JO  - Matematičeskie zametki
PY  - 2003
SP  - 676
EP  - 685
VL  - 74
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2003_74_5_a3/
LA  - ru
ID  - MZM_2003_74_5_a3
ER  - 
%0 Journal Article
%A A. A. Kovalevsky
%T Integrability of Solutions of Nonlinear Elliptic Equations with Right-Hand Sides from Logarithmic Classes
%J Matematičeskie zametki
%D 2003
%P 676-685
%V 74
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2003_74_5_a3/
%G ru
%F MZM_2003_74_5_a3
A. A. Kovalevsky. Integrability of Solutions of Nonlinear Elliptic Equations with Right-Hand Sides from Logarithmic Classes. Matematičeskie zametki, Tome 74 (2003) no. 5, pp. 676-685. http://geodesic.mathdoc.fr/item/MZM_2003_74_5_a3/

[1] Boccardo L., Gallouët T., “Non-linear elliptic and parabolic equations involving measure data”, J. Funct. Anal., 87 (1989), 149–169 | DOI | MR | Zbl

[2] Boccardo L., Gallouët T., “Nonlinear elliptic equations with right hand side measures”, Comm. Partial Differential Equations, 17 (1992), 641–655 | MR | Zbl

[3] Bénilan Ph., Boccardo L., Gallouët T., Gariepy R., Pierre M., Vazquez J. L., “An $L^1$-theory of existence and uniqueness of solutions of nonlinear elliptic equations”, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 22 (1995), 241–273 | MR | Zbl

[4] Boccardo L., Gallouët T., “Summability of the solutions of nonlinear elliptic equations with right hand side measures”, J. Convex Analysis, 3 (1996), 361–365 | MR | Zbl

[5] Kovalevskii A. A., “O summiruemosti reshenii nelineinykh ellipticheskikh uravnenii s pravymi chastyami iz klassov, blizkikh k $L^1$”, Matem. zametki, 70:3 (2001), 375–385 | Zbl

[6] Gilbarg D., Trudinger N. S., Elliptic partial differential equations of second order, Springer-Verlag, Berlin, 1983 | MR | Zbl