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
Full-text PDF Free Access
References |
Additional Information
W. R. Smythe, Static and dynamic electricity, 3rd ed., McGraw-Hill, New York, 1968
E. Durand, Électrostatique, Vol. II, Masson, Paris, 1966.
- Wolfgang K. H. Panofsky and Melba Phillips, Classical electricity and magnetism, 2nd ed., Addison-Wesley Series in Physics, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1962. MR 0135824
- Wolfgang K. H. Panofsky and Melba Phillips, Classical electricity and magnetism, 2nd ed., Addison-Wesley Series in Physics, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1962. MR 0135824
K. J. Binns and P. J. Lawrenson, Electric and magnetic field problems, Macmillan, New York, 1963, pp. 194 and 235
- 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
- V. I. Smirnov, A course of higher mathematics. Vol. III. Part two. Complex variables. Special functions, Pergamon Press, Oxford-Edinburgh-New York-Paris-Frankfurt; Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1964. Translated by D. E. Brown; Translation edited by I. N. Sneddon. MR 0182690
- L. V. Kantorovich and V. I. Krylov, Approximate methods of higher analysis, Interscience Publishers, Inc., New York; P. Noordhoff Ltd., Groningen, 1958. Translated from the 3rd Russian edition by C. D. Benster. MR 0106537
- 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
- Milton Abramowitz and Irene A. Stegun (eds.), Handbook of mathematical functions, with formulas, graphs and mathematical tables, 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. Fifth printing, with corrections. MR 0208798
- Ivar Stakgold, Boundary value problems of mathematical physics. Vol. II, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1968. MR 0243183
W. B. Joyce and S. H. Wemple, Steady-state junction-current distributions in thin resistive films on semiconductor junctions (solutions of ${\nabla ^2}\upsilon = \pm {e^\upsilon }$), J. Appl. Phys. 41, 3818–3830 (1970)
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).
W. R. Smythe, Static and dynamic electricity, 3rd ed., McGraw-Hill, New York, 1968
E. Durand, Électrostatique, Vol. II, Masson, Paris, 1966.
W. K. H. Panofsky and M. Phillips, Classical electricity and magnetism, 2nd ed., Addison-Wesley, Reading, Mass., 1962
W. K. H. Panofsky and M. Phillips, Classical electricity and magnetism, 2nd ed., Addison-Wesley, Reading, Mass., 1962, p. 69
K. J. Binns and P. J. Lawrenson, Electric and magnetic field problems, Macmillan, New York, 1963, pp. 194 and 235
G. F. Carrier, M. Krook and C. E. Pearson, Functions of a complex variable, McGraw-Hill, New York, 1966
V. I. Smirnov, A course of higher mathematics, Vol. III, Part II: Complex variables. Special functions, GITTL, Moscow, 1951; English transl., Pergamon Press, New York and Addison-Wesley, Reading, Mass., 1964, pp. 97 and 147
L. V. Kantorovič and V. I. Krylov, Approximate methods of higher analysis, Fizmatgiz, Moscow, 1962; English transl., Interscience, New York, 1958, pp. 523–542
P. P. Kufarev, On the method of numerical determination of the parameters in the Schwarz-Christoffel integral, Dokl. Akad. Nauk SSSR 57, 535–537 (1947) (Russian)
M. Abramowitz and I. A. Stegun (Editors) 5th printing with corrections, Handbook of mathematical functions with graphs, and mathematical tables, Nat. Bur. Standards Appl. Math. Ser., vol. 55, U. S. Government Printing Office, Washington, D. C., 1966, Eq. 15.3.1
I. Stakgold, Boundary value problems of mathematical physics, Vol. II, Macmillan, New York, 1968, pp. 164–165; 170 (cf. pp. 272–273)
W. B. Joyce and S. H. Wemple, Steady-state junction-current distributions in thin resistive films on semiconductor junctions (solutions of ${\nabla ^2}\upsilon = \pm {e^\upsilon }$), J. Appl. Phys. 41, 3818–3830 (1970)
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).
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Article copyright:
© Copyright 1970
American Mathematical Society
