Radially symmetric solutions of a Monge-Ampère equation arising in a reflector mapping problem

  • V. Oliker
  • P. Waltman
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1285)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    F. Brickell, L. Marder, and B.S. Westcott, The geometrical optics design of reflectors using complex coordinates, J. Phys. A: Math. Gen., Vol 10 (1977), 245–260.CrossRefGoogle Scholar
  2. [2]
    L. Caffarelli, L. Nirenberg, J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations, I. Monge-Ampère equation, Comm. on Pure and Appl. Math., 37(3) (1984), 369–402.MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    E.A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw Hill, New York, 1955.MATHGoogle Scholar
  4. [4]
    R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. II, Interscience Publishers, J. Wiley and Sons, New York, 1962.MATHGoogle Scholar
  5. [5]
    L. Eisenhart, Riemannian Geometry, Princeton Univ. Press, 1949.Google Scholar
  6. [6]
    P. Hartman and A. Wintner, On the third fundamental form of a surface, American J. of Math. 75 (1953), 298–334.MathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    J.B. Keller, The inverse scattering problem in geometical optics and the design of reflectors, IRE Transactions on antennas and propagation. 1958, 146–149.Google Scholar
  8. [8]
    L. Marder, Uniqueness in reflector mappings and the Monge-Ampère equation, Proc. R. Soc. London, A 378 (1981), 529–537.MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    A.P. Norris and B.S. Westcott, Computation of reflector surfaces for bivariate beamshaping in the elliptic case, J. Phys. A: Math. Gen. Vol. 9, No. 12 (1976), 2159–2169.CrossRefGoogle Scholar
  10. [10]
    B.S. Westcott, Shaped Reflector Antenna Design, Research Studies Press Ltd., Letchworth, Hertfordshire, England, 1983.Google Scholar
  11. [11]
    B.S. Westcott and A.P. Norris, Reflector synthesis for generalized far fields, J. Phys. A: Math. Gen. Vol. 8, No. 4, (1975), 521–532.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • V. Oliker
    • 1
  • P. Waltman
    • 1
  1. 1.Department of Mathematics and Computer ScienceEmory UniversityAtlanta

Personalised recommendations