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We study the uniqueness of solutions of Helmholtz equation for a problem that concerns wave propagation in waveguides. The classical radiation condition does not apply to our problem because the inhomogeneity of the index of refraction extends to infinity in one direction. Also, because of the presence of a waveguide, some waves propagate in one direction… (More)

- G. CIRAOLO
- 2015

We show that the oscillation of the scalar mean curvature of the boundary of a set controls in a quantitative way its distance from a finite family of disjoint tangent balls of equal radii. This result allows one to quantitatively describe the geometry of volume-constrained stationary sets in capillarity problems.

- G. CIRAOLO
- 2015

We prove that the boundary of a (not necessarily connected) bounded smooth set with constant nonlocal mean curvature is a sphere. More generally, and in contrast with what happens in the classical case, we show that the Lipschitz constant of the nonlocal mean curvature of such a boundary controls its C-distance from a single sphere. The corresponding… (More)

- Giulio Ciraolo
- 2009

We study the 2-D Helmholtz equation in perturbed stratified media, allowing the existence of guided waves. Our assumptions on the perturbing and source terms are not too restrictive. We prove two results. Firstly, we introduce a Sommerfeld-Rellich radiation condition and prove the uniqueness of the solution for the studied equation. Then, by careful… (More)

In this work we study the problem of wave propagation in a 3-D optical fiber∗. The goal is to obtain a solution for the time-harmonic field caused by a source in a cylindrically symmetric waveguide. The geometry of the problem, corresponding to an open waveguide, makes the problem challenging. To solve it, we construct a transform theory which is a… (More)

- Giulio Ciraolo, Francesco Gargano, Vincenzo Sciacca
- J. Comput. Physics
- 2013

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