5 citations · 6 across the 2 of their papers we have counts for
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The planar Least Gradient problem in convex domains: the discontinuous case
Piotr Rybka, Ahmad Sabra
We study the two dimensional least gradient problem in convex polygonal sets in the plane, . We show the existence of solutions when the boundary data are attained in the tr…
The planar Least Gradient problem in convex domains, the case of continuous datum
Piotr Rybka, Ahmad Sabra
We study the two dimensional least gradient problem in a convex polygonal set in the plane. We show existence of solutions when the boundary data are attained in the trace sense. D…
Refractor surfaces determined by near-field data
Aram Karakhanyan, Ahmad Sabra
In this paper we study the near-field refractor problem with point source at the origin and prescribed target on the given receiver surface . This nonvariational problem can be…
On the existence of dichromatic single element lenses
Cristian E. Gutierrez, 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…
The planar Least Gradient problem in convex domains
Piotr Rybka, Ahmad Sabra
We study the two dimensional least gradient problem in a convex, but not necessary strictly convex region. We look for solutions in the space of functions satisfying the bound…
Special cases of the planar least gradient problem
Wojciech Górny, Piotr Rybka, Ahmad Sabra
We study two special cases of the planar least gradient problem. In the first one, the boundary conditions are imposed on a part of the strictly convex domain. In the second case,…