Separation-of-variables solution from the Schwarz-Christoffel transformation

Author:
W. B. Joyce

Journal:
Quart. Appl. Math. **28** (1970), 383-390

DOI:
https://doi.org/10.1090/qam/99785

MathSciNet review:
QAM99785

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References | Additional Information

**[1]**W. R. Smythe,*Static and dynamic electricity*, 3rd ed., McGraw-Hill, New York, 1968**[2]**E. Durand,*Électrostatique*, Vol. II, Masson, Paris, 1966.**[3]**Wolfgang K. H. Panofsky and Melba Phillips,*Classical electricity and magnetism*, Second edition. Addison-Wesley Series in Physics, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1962. MR**0135824****[4]**Wolfgang K. H. Panofsky and Melba Phillips,*Classical electricity and magnetism*, Second edition. Addison-Wesley Series in Physics, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1962. MR**0135824****[5]**K. J. Binns and P. J. Lawrenson,*Electric and magnetic field problems*, Macmillan, New York, 1963, pp. 194 and 235**[6]**George F. Carrier, Max Krook, and Carl E. Pearson,*Functions of a complex variable: Theory and technique*, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR**0222256****[7]**V. I. Smirnov,*A course of higher mathematics. Vol. III. Part two. Complex variables. Special functions*, Translated by D. E. Brown. Translation edited by I. N. Sneddon, Pergamon Press, Oxford-Edinburgh-New York-Paris-Frankfurt; Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1964. MR**0182690****[8]**L. V. Kantorovich and V. I. Krylov,*Approximate methods of higher analysis*, Translated from the 3rd Russian edition by C. D. Benster, Interscience Publishers, Inc., New York; P. Noordhoff Ltd., Groningen, 1958. MR**0106537****[9]**P. P. Kufarev,*On a method of numerical determination of the parameters in the Schwarz-Christoffel integral*, Doklady Akad. Nauk SSSR (N. S.)**57**(1947), 535–537 (Russian). MR**0022911****[10]***Handbook of mathematical functions, with formulas, graphs and mathematical tables*, Edited by Milton Abramowitz and Irene A. Stegun. Fifth printing, with corrections. National Bureau of Standards Applied Mathematics Series, Vol. 55, National Bureau of Standards, Washington, D.C., (for sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 20402), 1966. MR**0208798****[11]**Ivar Stakgold,*Boundary value problems of mathematical physics. Vol. II*, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1968. MR**0243183****[12]**W. B. Joyce and S. H. Wemple,*Steady-state junction-current distributions in thin resistive films on semiconductor junctions*(*solutions of*), J. Appl. Phys.**41**, 3818-3830 (1970)**[13]**Further discussions of asymptotic solutions near corners appear in: J. A. Lewis and E. Wasserstrom,*The field singularity at the edge of an electrode on a semiconductor surface*, Bell System Tech. J.**49**, 1183-94 (1970); S. R. Lehman,*Developments at an analytic corner of solutions of elliptic partial differential equations*, J. Math. Mech.**8**, 727-760 (1959); W. R. Wasow,*Asymptotic development of the solution of Dirichlet's problem at analytic corners*, Duke Math. J.**24**, 47-56 (1957).

Additional Information

DOI:
https://doi.org/10.1090/qam/99785

Article copyright:
© Copyright 1970
American Mathematical Society