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Volumn 13, Issue 1, 2007, Pages 93-106

Existence of optimal maps in the reflector-type problems

Author keywords

Mass transport; Monge ampere equation; Reflector problem

Indexed keywords

GEOMETRICAL OPTICS; MASS TRANSFER; PROBABILITY; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

EID: 33947108877     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2006017     Document Type: Article
Times cited : (26)

References (24)
  • 3
    • 0039984892 scopus 로고
    • Weak solutions of one inverse problem in geometric optics
    • Preprint
    • L.A. Caffarelli and V.I. Oliker, Weak solutions of one inverse problem in geometric optics. Preprint (1994).
    • (1994)
    • Caffarelli, L.A.1    Oliker, V.I.2
  • 4
    • 33947180862 scopus 로고    scopus 로고
    • L.A. Caffarelli and S. Kochengin and V.I. Oliker, On the numerical solution of the problem of reflector design with given far-field scattering data. Cont. Math. 226 (1999) 13-32.
    • L.A. Caffarelli and S. Kochengin and V.I. Oliker, On the numerical solution of the problem of reflector design with given far-field scattering data. Cont. Math. 226 (1999) 13-32.
  • 6
    • 0001103156 scopus 로고    scopus 로고
    • The geometry of optimal transportation
    • W. Gangbo and R.J. McCann, The geometry of optimal transportation. Acta Math. 177 (1996) 113-161.
    • (1996) Acta Math , vol.177 , pp. 113-161
    • Gangbo, W.1    McCann, R.J.2
  • 7
    • 0344032898 scopus 로고    scopus 로고
    • Shape recognition via Wasserstein distance
    • W. Gangbo and R. McCann, Shape recognition via Wasserstein distance. Quart. Appl. Math. 58 (2000) 705-737.
    • (2000) Quart. Appl. Math , vol.58 , pp. 705-737
    • Gangbo, W.1    McCann, R.2
  • 8
    • 11044234672 scopus 로고    scopus 로고
    • Optical design of single reflector systems and the Monge-Kantorovich mass transfer problem
    • T. Glimm and V.I. Oliker, Optical design of single reflector systems and the Monge-Kantorovich mass transfer problem. J. Math. Sci. 117 (2003) 4096-4108.
    • (2003) J. Math. Sci , vol.117 , pp. 4096-4108
    • Glimm, T.1    Oliker, V.I.2
  • 9
    • 11044226730 scopus 로고    scopus 로고
    • Optical design of two-reflector systems, the Monge-Kantorovich mass transfer problem and Fermat's principle
    • T. Glimm and V.I. Oliker, Optical design of two-reflector systems, the Monge-Kantorovich mass transfer problem and Fermat's principle. Indiana Univ. Math. J. 53 (2004) 1255-1278.
    • (2004) Indiana Univ. Math. J , vol.53 , pp. 1255-1278
    • Glimm, T.1    Oliker, V.I.2
  • 10
    • 0012802489 scopus 로고    scopus 로고
    • On a Monge-Ampère equation arising in geometric optics
    • Pengfei Guan and Xu-Jia Wang, On a Monge-Ampère equation arising in geometric optics J. Differential Geometry 48 (1998) 205-223.
    • (1998) J. Differential Geometry , vol.48 , pp. 205-223
    • Guan, P.1    Wang, X.2
  • 11
    • 0000485730 scopus 로고
    • Duality theorems for marginal problems
    • H.G. Kellerer, Duality theorems for marginal problems. Z. Wahrsch. Verw. Gebiete 67 (1984) 399-432.
    • (1984) Z. Wahrsch. Verw. Gebiete , vol.67 , pp. 399-432
    • Kellerer, H.G.1
  • 12
  • 13
    • 0021421774 scopus 로고
    • On the optimal mapping of distributions
    • M. Knott and C.S. Smith, On the optimal mapping of distributions. J. Optim. Theory Appl. 43 (1984) 39-49.
    • (1984) J. Optim. Theory Appl , vol.43 , pp. 39-49
    • Knott, M.1    Smith, C.S.2
  • 14
    • 0040577813 scopus 로고
    • Differential-geometric methods in design of reflector antennas
    • E. Newman and V.I. Oliker, Differential-geometric methods in design of reflector antennas. Symposia Mathematica 35 (1994) 205-223.
    • (1994) Symposia Mathematica , vol.35 , pp. 205-223
    • Newman, E.1    Oliker, V.I.2
  • 15
    • 10644238931 scopus 로고
    • Computation of reflector surfaces for bivariate beamshaping in the elliptic case
    • A.P. Norris and B.S. Westcott, Computation of reflector surfaces for bivariate beamshaping in the elliptic case. J. Phys. A: Math. Gen 9 (1976) 2159-2169.
    • (1976) J. Phys. A: Math. Gen , vol.9 , pp. 2159-2169
    • Norris, A.P.1    Westcott, B.S.2
  • 16
    • 33947113259 scopus 로고    scopus 로고
    • V.I. Oliker and P. Waltman, Radially symmetric solutions of a Monge-Ampere equation arising in a reflector mapping problem. Proc. U AB Int. Conf. on Diff. Equations and Math. Physics, edited by 1. Knowles and Y. Saito, Springer. Lect. Notes Math. 1285 (1987) 361-374.
    • V.I. Oliker and P. Waltman, Radially symmetric solutions of a Monge-Ampere equation arising in a reflector mapping problem. Proc. U AB Int. Conf. on Diff. Equations and Math. Physics, edited by 1. Knowles and Y. Saito, Springer. Lect. Notes Math. 1285 (1987) 361-374.
  • 18
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton
    • R.T. Rockafellar, Convex Analysis. Princeton University Press, Princeton (1970).
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 20
    • 0000012825 scopus 로고
    • On Hoeffding-Fréchet bounds and cyclic monotone relations
    • C. Smith and M. Knott, On Hoeffding-Fréchet bounds and cyclic monotone relations. J. Multivariate Anal. 40 (1992) 328-334.
    • (1992) J. Multivariate Anal , vol.40 , pp. 328-334
    • Smith, C.1    Knott, M.2
  • 21
    • 0038552249 scopus 로고    scopus 로고
    • On design of a reflector antenna
    • X.-J. Wang, On design of a reflector antenna. Inverse Problems 12 (1996) 351-375.
    • (1996) Inverse Problems , vol.12 , pp. 351-375
    • Wang, X.-J.1
  • 22
    • 3042583367 scopus 로고    scopus 로고
    • On design of a reflector antenna II
    • X.-J. Wang, On design of a reflector antenna II. Calculus of Variations and PDE's 20 (2004) 329-341.
    • (2004) Calculus of Variations and PDE's , vol.20 , pp. 329-341
    • Wang, X.-J.1
  • 24
    • 0002015997 scopus 로고
    • Open problems in geometry, in Differential Geometry. Part 1: Partial Differential Equations on Manifolds (Los Angeles, 1990)
    • R. Greene and S.T. Yau Eds, Amer. Math. Soc
    • S.T. Yau, Open problems in geometry, in Differential Geometry. Part 1: Partial Differential Equations on Manifolds (Los Angeles, 1990), R. Greene and S.T. Yau Eds., Proc. Sympos. Pure Math., Amer. Math. Soc. 54 (1993) 1-28.
    • (1993) Proc. Sympos. Pure Math , vol.54 , pp. 1-28
    • Yau, S.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.