Zobrazeno 1 - 10
of 90
pro vyhledávání: '"Cristian E. Gutiérrez"'
Autor:
Henok Mawi, Cristian E. Gutiérrez
Publikováno v:
Applied Mathematics & Optimization. 84:1877-1902
A numerical scheme is presented to solve the one source near field refractor problem to arbitrary precision and it is proved that the scheme terminates in a finite number of iterations. The convergence of the algorithm depends upon proving appropriat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::134de9df88d1a9fce71ddf5d56939263
https://doi.org/10.1007/s00245-021-09814-3
https://doi.org/10.1007/s00245-021-09814-3
Publikováno v:
Annales de l'Institut Henri Poincaré C, Analyse non linéaire. 38:577-600
We establish local C 1 , α estimates for one source near field refractors under structural assumptions on the target, and with no assumptions on the smoothness of the densities.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7d6e83a3eebfe7b7149c986f2f6ecf2f
https://doi.org/10.1016/j.anihpc.2020.08.002
https://doi.org/10.1016/j.anihpc.2020.08.002
Publikováno v:
Proceedings of the London Mathematical Society. 122:537-568
Using optimal mass transport arguments, we prove weighted Sobolev inequalities of the form \[\left(\int_E |u(x)|^q\,\omega(x) \,dx\right)^{1/q}\leq K_0\,\left(\int_E |\nabla u(x)|^p\,\sigma(x)\,dx\right)^{1/p},\ \ u\in C_0^\infty(\mathbb R^n),\ \ \ \
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::167fec851f8fff254ea0188322a5e43c
https://doi.org/10.1112/plms.12384
https://doi.org/10.1112/plms.12384
For cost functions c(x, y) = h(x- y) , with h∈ C2(Rn\ { 0 }) ∩ C1(Rn) homogeneous of degree p> 1 , we show L∞-estimates of Tx- x on balls, where T is an h-monotone map. Estimates for the interpolating mappings Tt= t(T- I) + I are deduced from t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b8277fc72d11691d890662a06f980ac5
https://hdl.handle.net/11585/895226
https://hdl.handle.net/11585/895226
This paper provides a theoretical and numerical approach to show existence, uniqueness, and the numerical determination of metalenses refracting radiation with energy patterns. The theoretical part uses ideas from optimal transport and for the numeri
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4df41877f3fdc1f55978d59936343083
Autor:
Cristian E. Gutiérrez
This book concerns the theory of optimal transport (OT) and its applications to solving problems in geometric optics. It is a self-contained presentation including a detailed analysis of the Monge problem, the Monge-Kantorovich problem, the transship
Publikováno v:
Nonlinear Analysis. 157:123-145
The far field refractor problem with a discrete target is solved with a numerical scheme that uses and simplify ideas from Caffarelli, Kochengin and Oliker. A numerical implementation is carried out and examples are shown.
Comment: 28 pages, 9 f
Comment: 28 pages, 9 f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ac4d8533ca38f2085db90a96abef21a4
https://doi.org/10.1016/j.na.2017.03.009
https://doi.org/10.1016/j.na.2017.03.009
Publikováno v:
Nonlinear Analysis. 142:1-25
We consider the parallel refractor problem when the planar radiating source lies in a medium having higher refractive index than the medium in which the target is located. We prove local C 1 , α estimates for parallel refractors under suitable geome
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a1706d4b2856b2b289ed85ff970b735a
https://doi.org/10.1016/j.na.2016.04.001
https://doi.org/10.1016/j.na.2016.04.001
A metasurface is a surface, tipically a plane, on which a function called phase discontinuity is chosen so that the metasurface produces a desired reflection or refraction job. We derive the equations that the phase discontinuity function must satisf
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::28fb7c1592f2f21cb8ff0a936b439211
http://arxiv.org/abs/1805.00722
http://arxiv.org/abs/1805.00722
Autor:
Cristian E. Gutiérrez, Ahmad Sabra
Due to dispersion, light with different wavelengths, or colors, is refracted at different angles. Our purpose is to determine when is it possible to design a lens made of a single homogeneous material so that it refracts light superposition of two co
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e40aad19d8da17c4d5e20352d44fab0c
http://arxiv.org/abs/1801.07223
http://arxiv.org/abs/1801.07223