Skip to main content

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

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1285))

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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.

    Article  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  3. E.A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw Hill, New York, 1955.

    MATH  Google Scholar 

  4. R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. II, Interscience Publishers, J. Wiley and Sons, New York, 1962.

    MATH  Google Scholar 

  5. L. Eisenhart, Riemannian Geometry, Princeton Univ. Press, 1949.

    Google Scholar 

  6. P. Hartman and A. Wintner, On the third fundamental form of a surface, American J. of Math. 75 (1953), 298–334.

    Article  MathSciNet  MATH  Google Scholar 

  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. L. Marder, Uniqueness in reflector mappings and the Monge-Ampère equation, Proc. R. Soc. London, A 378 (1981), 529–537.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  10. B.S. Westcott, Shaped Reflector Antenna Design, Research Studies Press Ltd., Letchworth, Hertfordshire, England, 1983.

    Google Scholar 

  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.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Ian W. Knowles Yoshimi Saitō

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Oliker, V., Waltman, P. (1987). Radially symmetric solutions of a Monge-Ampère equation arising in a reflector mapping problem. In: Knowles, I.W., Saitō, Y. (eds) Differential Equations and Mathematical Physics. Lecture Notes in Mathematics, vol 1285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080616

Download citation

  • DOI: https://doi.org/10.1007/BFb0080616

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18479-9

  • Online ISBN: 978-3-540-47983-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics