The study of boundary value problems for a singular $B$-elliptic equation by the method of potentials

E. V. Chebatoreva

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2010), pp. 88-90

Résumé

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, $0<\alpha<1$ and $k>0$ are constants, $p\ge3$. We prove the unique solvability of these problems.

Détail

Keywords: Bessel operator, Dirichlet problem, Neumann problem, method of potentials.
Mots-clés : $B$-elliptic equation

Bibliographie

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[2] Mikhlin S. G., Lineinye uravneniya v chastnykh proizvodnykh, Vysshaya shkola, M., 1977, 432 pp. | MR