Geodesic
The study of boundary value problems for a~singular $B$-elliptic equation by the method of potentials
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2010), pp. 88-90

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In this paper we apply the method of potentials for studying the Dirichlet and Neumann boundary value problems for a $B$-elliptic equation in the form $$ \Delta_{x''}u+B_{x_{p-1}}u+x_p^{-\alpha}\frac\partial{\partial x_p}\left({x_p^\alpha\frac{\partial u}{\partial x_p}}\right)=0, $$ where $\Delta_{x''}=\sum^{p-2}_{j=1}\frac{\partial^2}{\partial x_j^2}$, $B_{x_{p-1}}=\frac{\partial^2}{\partial x_{p-1}^2}+\frac k{x_{p-1}}\frac\partial{\partial x_{p-1}}$ is the Bessel operator, $0\alpha1$ and $k>0$ are constants, $p\ge3$. We prove the unique solvability of these problems.
Keywords: Bessel operator, Dirichlet problem, Neumann problem, method of potentials.
Mots-clés : $B$-elliptic equation 
@article{IVM_2010_5_a10,
     author = {E. V. Chebatoreva},
     title = {The study of boundary value problems for a~singular $B$-elliptic equation by the method of potentials},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {88--90},
     publisher = {mathdoc},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_5_a10/}
}
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E. V. Chebatoreva. The study of boundary value problems for a~singular $B$-elliptic equation by the method of potentials. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2010), pp. 88-90. http://geodesic.mathdoc.fr/item/IVM_2010_5_a10/