Reflector problem in \({\mathbb R^n}\) endowed with non-Euclidean norm

DOI10.1007/s00205-009-0221-1zbMath1173.78003OpenAlexW2007183351MaRDI QIDQ834765

Qingbo Huang, Luis A. Caffarelli

Publication date: 27 August 2009

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-009-0221-1

zbMATH Keywords

optimal mass transporthomogeneous nonisotropic mediumreflector problem

Mathematics Subject Classification ID

Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10) Variational methods applied to problems in optics and electromagnetic theory (78M30)

Related Items (6)

The refractor problem in reshaping light beams ⋮ On the \(L_q\)-reflector problem in \(\mathbb{R}^n\) with non-Euclidean norm ⋮ On the generalized \(L_q\)-reflector inverse problem with variational methods ⋮ The near field refractor ⋮ An overview of mathematical modeling of geometric optics problems involving refraction ⋮ Refractors in anisotropic media associated with norms

Cites Work

• Weak solutions of one inverse problem in geometric optics
• On the limits of periodic Riemannian metrics
• On a Monge-Ampère equation arising in geometric optics
• On the design of a reflector antenna. II
• On the regularity of reflector antennas
• Existence of optimal maps in the reflector-type problems
• On the design of a reflector antenna
• A Minkowski-style theorem for focal functions of compact convex reflectors
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