Geodesic
Solvability of the Dirichlet problem for degenerate quasilinear elliptic equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 178-190 
P. Z. Mkrtychyan. Solvability of the Dirichlet problem for degenerate quasilinear elliptic equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 178-190. http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a14/
@article{ZNSL_1982_115_a14,
     author = {P. Z. Mkrtychyan},
     title = {Solvability of the {Dirichlet} problem for degenerate quasilinear elliptic equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {178--190},
     year = {1982},
     volume = {115},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a14/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In a bounded domain of the n-dimensional $$ \sum_{i=1}^n\frac\partial{\partial x_i}(a^{l_i}(u)|u_{x_i}|^{m_i-2}u_{x_i})=f(x), $$ where $x=(x_1,\dots,x_n)$, $l_i\ge0$, $m_i>1$, the function $f$ is summable with some power, the nonnegative continuous function $a(u)$ vanishes at a finite number of points and satisfies $\varliminf_{|u|\to\infty}a(u)>0$. One proves the existence of bounded generalized solutions with a finite integral $$ \int_\Omega\sum_{i=1}^na^{l_i}(u)|u_{x_i}|^{m_i}\,dx $$ of the Dirichlet problem with zero boundary conditions.