An Inverse Problem for the Refractive Surfaces with Parallel Lighting

DOI10.1137/140964941zbMath1335.35086arXiv1403.2454OpenAlexW1523300201MaRDI QIDQ2790394

Aram L. Karakhanyan

Publication date: 4 March 2016

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.2454

zbMATH Keywords

Monge-Ampère-type equationsantenna designparallel refractor

Mathematics Subject Classification ID

Antennas, waveguides in optics and electromagnetic theory (78A50) Weak solutions to PDEs (35D30) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Geometric optics (78A05) Monge-Ampère equations (35J96)

Related Items (9)

\(C^{1, \alpha}\) estimates for the parallel refractor ⋮ 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 ⋮ On the existence of dichromatic single element lenses ⋮ Freeform lens design for scattering data with general radiant fields ⋮ Refractor surfaces determined by near-field data ⋮ On the second boundary value problem for Monge-Ampère type equations and geometric optics ⋮ An overview of mathematical modeling of geometric optics problems involving refraction ⋮ Refractors in anisotropic media associated with norms

Cites Work

• On the local theory of prescribed Jacobian equations
• Existence and regularity of the reflector surfaces in \(\mathbb R^{n+1}\)
• The near field refractor
• Regularity for the near field parallel refractor and reflector problems
• On the classical solvability of near field reflector problems
• On the regularity of solutions of optimal transportation problems
• On strict convexity and continuous differentiability of potential functions in optimal transportation
• On the reflector shape design
• Oblique boundary value problems for equations of Monge-Ampère type
• Light reflection is nonlinear optimization
• Regularity of potential functions of the optimal transportation problem
• On the Dirichlet problem for Monge-Ampère type equations
• Polar factorization and monotone rearrangement of vector‐valued functions
• The Regularity of Mappings with a Convex Potential
• On the design of a reflector antenna
• The Parallel Refractor
• The Monge-Ampère equation
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: An Inverse Problem for the Refractive Surfaces with Parallel Lighting