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References
R.A. Adams,Sobolev Spaces, Academic Press, New York, 1975.
H. Brenner and R.G. Cox,The resistance to a particle of arbitrary shape in translational motion at small Reynolds numbers, J. Fluid Mech., 17 (1963), pp. 561–595.
I-D. Chang and R. Finn,On the solutions of a class of equations occurring in continuum mechanics, with application to the Stokes paradox, Arch. Rat. Mech. Anal., 7 (1961), pp. 388–401.
J.D. Cole,Perturbation Methods in Applied Mathematics, Blaisdell, Waltham, Massachusetts, 1968.
M. van Dyke,Perturbation Methods in Fluid Mechanics, Academic Press, New York, 1964.
R. Finn,On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems, Arch. Rat. Mech. Anal., 19 (1965), pp. 363–406.
I.M. Gelfand and G.E. Schilow,Verallgemeinerte Funktionen (Distributionen) I, Deutscher Verlag d. Wiss., Berlin, 1960.
G.C. Hsiao,Singular perturbation of an exterior Dirichlet problem, SIAM J. Math. Anal., 9 (1978), pp. 160–184.
G.C. Hsiao,Integral representations of solutions for two-dimensional viscous flow problems, Conference on: Integral Equation Methods in Engineering, Oberwolfach, 1980. To appear.
G.C. Hsiao, P. Kopp and W.L. Wendland,A Galerkin collocation method for some integral equations of the first kind, Computing, 25 (1980), pp. 89–130.
G.C. Hsiao, P. Kopp and W.L. Wendland,Some applications of a Galerkin-collocation method for integral equations of the first kind. To appear.
G.C. Hsiao and R.C. Mac Camy,Solution of boundary value problems by integral equations of the first kind, SIAM Rev., 15 (1973), pp. 687–705.
G.C. Hsiao and W.L. Wendland,A finite element method for some integral equations of the first kind, J. Math. Anal. Appl., 58 (1977), pp. 449–481.
R.P. Kanwal,Linear Integral Equations, Academic Press, New York, 1971.
S. Kaplun and P.A. Lagerstrom,Asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers, J. Math. Mech., 6 (1957), pp. 585–593.
J.J. Kohn and L. Nirenberg,An algebra of pseudo-differential operators, Comm. Pure Appl. Math., 18 (1965), pp. 269–305.
O.A. Ladyzhenskaya,The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York, 1963.
J.R.A. Pearson and I. Proudman,Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder, J. Fluid Mech., 2 (1957), pp. 237–262.
R. Seeley,Topics in pseudo-differential operators, in: Pseudo-Differential Operators, C.I.M.E. (L. Nirenberg ed.), Edizioni Cremonese, Roma, 1969.
E. Stephan and W.L. Wendland,Remarks to Galerkin and least squares methods with finite elements for general elliptic problems, Lecture Notes Math., No. 564, pp. 461–471, Springer-Verlag, Berlin, 1976, and Manuscripta Geodaetica, 1 (1976), pp. 93–123.
W.L. Wendland,Lectures on the approximation of integral equations, given at the Ecole Polytechnique, 1976, and at the Dept. Mathematics, Oregon State University in Corvallis, 1977. Unpublished Lecture Notes.
W.L. Wendland,On Galerkin collocation methods for integral equations of elliptic boundary value problems, in: Numerical Treatment of Integral Equations, ISNM 53 (J. Albrecht and L. Collatz ed.), Birkhäuser, Basel, 1980.
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Fischer, T.M. An integral equation procedure for the exterior three-dimensional slow viscous flow. Integr equ oper theory 5, 490–505 (1982). https://doi.org/10.1007/BF01694049
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DOI: https://doi.org/10.1007/BF01694049