On the design of a reflector antenna

Inverse Problems

Volumn 12, Issue 3, 1996, Pages 351-375

  Wang, Xu Jia ^a,b  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038552249     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/12/3/013     Document Type: Article

References (19)

1. Brickell F, Marder L. and Wstcott B 1977 The geometrical optics design of reflectors using complex coordinates J. Phys. A: Math. Gen. 10 245-60
2. Caffarelli L. A. Nirenberg L. and Spruck J 1984 The Dirichlet problem for nonlinear second order elliptic equations, I. Monge-Ampère equations Commun. Pure Appl. Math. 37 369-402
3. j) = F(x, u) Commun, Pure Appl. Math. 30 41-68
4. Engl H W and Neubauer A 1991 Reflector design as an inverse problem Proc. 5th Eur. Conf. for Mathematics in Industry ed M Heiliö (Teubner: kluwer) pp 13-24
5. Gilbarg D and Trudinger N S 1983 Elliptic Partial Differential Equations of Second Order (Berlin: Springer) 529-37
6. Neubauer A 1994 The Iterative Solution of a Nonlinear Inverse Problem from Industry, Desing of Reflectors (Curves and Surfaces II) ed P S Laurent, A Le Mháulé and L Shuwake (Boston: AKPetes) pp 335-42
7. Norris A P and Westcott B S 1976 Computation of reflector surface for bivariate beamshaping in the elliptic case J. Phys. A: Math. Gen. 9 2159-69
8. Oliker V I 1987 Near radially symmetric solutions of an inverse problem in geometric optics Inverse Problems 3 743-56
9. Oliker V I 1989 On reconstructing a reflecting surface from the scattering data in the geometric optics approximation Inverse Problems 5 751-65
10. Oliker V I and Waltman P 1987 Radially symmetric solutions of a Monge-Ampère equation arising in a reflector mapping problem Proc. Int. Conf. on Differential Equation and Mathematical Physics ed I Knowles and I Saito (New York: Springer)
11. Pogorelov A V 1964 Monge-Ampère Equations of Elliptic Type (Groningen: Noordholf)
12. Schulz F 1990 Regularity Theory for Quasilinear Elliptic Systems and Monge-Ampère Equation in Two Dimension (Lecture Notes in Mathematics 1445) (Berlin: Springer)
13. Wang X J 1992 Oblique derivative problems for Monge-Ampère equations Chin. Ann. Math. 13 41-50
14. Westcott B S 1983 Shaped Reflector Antenna Design (Letchworth: Research Studies Press)
15. Westcott B S and Norris A P 1975 Reflector synthesis for generalized far fields J. Phys. A: Math. Gen. 8 521-32
16. Rauch J and Taylor B A 1977 The Dirichlet problem for the multidimentional Monge-Ampère equation Rocky Mountain J. Math. 7 345-64
17. Oliker V and Newman E 1993 On the energy conservation equation in the reflector mapping problem Appl. Math. Lett. 6 91-5
18. Newman E and Oliker V Differential-geometric methods in the design of reflector antennas Symp. Math. XXXV 205-23
19. Caffarelli L. and Oliker V Weak solutions of the inverse problem in geometric optics Preprint