相关论文: $C^{1,\alpha}$ estimates for the parallel refracto…
We prove local $C^{1,\alpha}$ estimates of solutions for the parallel refractor and reflector problems under local assumptions on the target set $\Sigma$, and no assumptions are made on the smoothness of the densities.
We establish local $C^{1,\alpha}$ estimates for one source near field refractors under structural assumptions on the target, and with no assumptions on the smoothness of the densities.
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…
We present an abstract method in the setting of compact metric spaces which is applied to solve a number of problems in geometric optics. In particular, we solve the one source near field refraction problem. That is, we construct surfaces…
In a recently proposed approach to testing models of inflation by Cosmic Microwave Background (CMB) radiation the reheating temperature is directly expressed in terms of the CMB observables. Its model independent bounds translate in a given…
The modified scalar boson propagator due to the presence of a hyperplane semi-transparent mirror is computed. From this, the classical interaction between static charges and the mirror is investigated employing delta-like potentials and…
We study the regularity of solutions to the fully nonlinear thin obstacle problem. We establish local $C^{1,\alpha}$ estimates on each side of the smooth obstacle, for some small $\alpha > 0$. Our results extend those of Milakis-Silvestre…
We consider critical points of the geometric obstacle problem on vectorial maps $u: \mathbb{B}^2 \subset \mathbb{R}^2 \to \mathbb{R}^N$ \[ \int_{\mathbb{B}^2} |\nabla u|^2 \quad \mbox{subject to $u \in \mathbb{R}^N \backslash…
After Planck 2013, a broad class of inflationary models called \alpha-attractors was developed which has universal observational predictions. For small values of the parameter \alpha, the models have good consistency with the recent CMB…
Cosmological $\alpha$-attractors are a compelling class of inflationary models. They lead to universal predictions for large-scale observables, broadly independent from the functional form of the inflaton potential. In this work we derive…
Recently it has been proposed that a planar slab of material, for which both the permittivity and permeability have the values of -1, could bring not only the propagating fields associated with a source to a focus, but could also refocus…
A simple analytic method of estimating the error involved in using an approximate boundary condition for diffuse radiation in two adjoining scattering media with differing refractive index is presented. The method is based on asymptotic…
We have considered a semi-infinite crack embedded in a transversely isotropic medium and studied two special cases, one, in which the axis of symmetry is normal to the crack face and the wave incidence is arbitrary and another, in which the…
We study a Caputo time fractional degenerate diffusion equation which we prove to be equivalent to the fractional parabolic obstacle problem, showing that its solution evolves for any $\alpha\in(0,1)$ to the same stationary state, the…
We introduce a model to design reflectors that take into account the inverse square law for radiation. We prove existence of solutions, both in the near and far field cases, when the input and output energies are prescribed.
In this paper we study the near-field refractor problem with point source at the origin and prescribed target on the given receiver surface $\Sigma$. This nonvariational problem can be studied in the framework of prescribed Jacobian…
We provide an explicit geometric algorithm involving only ruler and compass constructions in order to specify the specular reflection point on the surface of a reflecting sphere of radius $r$ given two focal points $A$ and $B$ lying outside…
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…
Coherent illumination reflected by a remote target may be secondarily scattered by intermediate objects or materials. Here we show that phase retrieval on remotely observed images of such scattered fields enables imaging of the illuminated…
We consider the isoperimetric problem in $\mathbb R^n$ with density for the planar case $n=2$. We show that, if the density is ${\rm C}^{0,\alpha}$, then the boundary of any isoperimetric is of class ${\rm C}^{1,\frac \alpha{3-2\alpha}}$.…