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On ‘Power‐logarithmic’ Solutions to the Dirichlet Problem for the Stokes System in a Dihedral Angle
Author(s) -
Kozlov V. A.,
Maz'ya V. G.
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19970310)20:4<315::aid-mma861>3.0.co;2-m
Subject(s) - mathematics , dirichlet problem , logarithm , dihedral angle , mathematical analysis , homogeneous , stokes problem , dirichlet distribution , dihedral group , dirichlet conditions , dirichlet's principle , combinatorics , physics , finite element method , hydrogen bond , molecule , thermodynamics , boundary value problem , quantum mechanics , group (periodic table)
The Dirichlet problem for the Stokes system in a dihedral angle is considered. An explicit description of special solutions to the homogeneous problem which have the form\documentclass{minimal} \begin{document} \begin{eqnarray*} U(x) &=&\left| x\right| ^\lambda \sum_{0\leq k\leq \kappa }\frac{(\log \left| x\right|)^{\kappa -k}}{(\kappa -k)!}u^{(k)}(x/\left| x\right|), \\ P(x) &=&\left| x\right| ^{\lambda -1}\sum_{0\leq k\leq \kappa }\frac{(\log \left| x\right|)^{\kappa -k}}{(\kappa -k)!}p^{(k)}(x/\left| x\right|) \end{eqnarray*} \end{document}is given. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.