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

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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/}
}
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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/