Resonance will turn out to be one important factor that could cause increased radiation at certain spots, so let's take a minute to understand this.
The same effect that we observe in resonant cavity with microwaves is observed with mechanical waves in closed pipes (such as a clarinet). This is because this effects derive from the "wavy" nature of these phenomena. What this mean is that they can be at some point described by in terms of a solution of the wave equation.
Even though the physical interpretations change, we can get a good understanding of this by looking (image extracted from here, where you can also read more about sound waves in instruments) at what happens at a pipe with one closed side (at the right)
As one can see in the image above, there's two harmonics shown at the pipe with one side closed. What happens is that you get resonance at the frequency of these countless possible harmonics. The problem here is that if two equal waves going in opposite directions interfere with each other with constant phase = 0, (Nussenzveig, H. M. (2002). Curso de Física Básica. São Paulo: Edgar Blucher, pp.110-111) you can get a stationary wave where the nodes achieve twice the amplitude (That's why you can get higher intensity spots from the cellphone signal in comparison to the case where you ar not in a closed metal box creating this resonant pattern). Take a look to what happens to the black line (standing wave composed of the other two waves going in opposite directions:
In the animation above "AN" means antinode and "N" means node. This (node) is where you would get your "hot spots" in a cavity chamber.
The geometry of the clarinet will create conditions that forces the air pressure waves to behave in a specific manner. This specific manner is called stationary wave. An stationary wave is a wave in which its nodes and antinodes (peaks and valleys in intensity) do not move spatially.
As you can see here
A standing wave pattern is a vibrational pattern created within a medium when the vibrational frequency of the source causes reflected waves from one end of the medium to interfere with incident waves from the source. This
interference occurs in such a manner that specific points along the medium appear to be standing still. Because the observed wave pattern is characterized by points that appear to be standing still, the pattern is often called a standing wave pattern. Such patterns are only created within the medium at specific frequencies of vibration. These frequencies are known as harmonic frequencies, or merely harmonics. At any frequency other than a harmonic frequency, the interference of reflected and incident waves leads to a resulting disturbance of the medium that is irregular and non-repeating.
So, what does this have to do with resonant cavities and elevators? An elevator is an enclosed metal box, which gives the physical conditions to generate stationary wave inside it (For specific frequencies in specific modes - given by the solutions to the differential equations in those boundaries conditions. Or you could say: because math.)
Reference for what i just said can be found
here at page 75 in a simple case overview
here for more comprehensive (and much more understandable in my opinion) overview at page 285
But I can show to you (I won't reference this because i just took a print from a slide of my professor) that you will get modes (equivalent to the harmonics at the other example. Also this shows only TM, there is TE too. You can't get TEM here) like this:
In the last link you can see that the fields that will resonate in a cavity and will have a sinusoidal aspect along the space. Such as in the mode TE 10L:
This means that in some points it will have higher intensity and others lower, nodes and antinodes, (because waves are interfering constructively and destructively) such as in the clarinet example.
Note that this effect depends mainly by the frequencies that are being inserted on the cavity. Such as said before:
At any frequency other than a harmonic frequency, the interference of reflected and incident waves lead to a resulting disturbance of the medium that is irregular and non-repeating.
To my understanding, if you insert frequencies that do not resonate well at the cavity, you will end up not having this effect in its highest intensity because you need to have integer multiples of half the wave length to fit inside the chamber.
In my previous post I was speculating about why could someone be concerned about radiation intensity inside an elevator. So the point that I was trying to make was that those two phenomena ( the cellphone increase in its potency radiation and resonance ) could be the cause for those concerned warnings in Israel cited by OP. Nevertheless, I had no idea if these effect would be potentially harmful or not.
So, I went online just now and found these two papers.
The first was:
The abstract for this first one:
The effects of the radio frequency human exposure to mobile phone, inside both partially and fully enclosed metallic elevators,have been analyzed. It has been found that the evaluated peak Specific Absorption Rate (SAR) and the whole body absorption power are in-creased only by a small percentage inside the partial enclosures as compared to the free space environment; whereas inside the full enclosure, the peak SAR and the whole body absorption power are significantly increased. The analysis suggest that the reason of such a high level of RF energy absorption inside a fully enclosed metallic elevator is mainly because of the resonance effect.
The other paper was:
Human exposure by mobile phones in enclosed areas such as train carriages, elevators, and cars is considered. Equivalent power density and whole body specific absorption rate (SAR) are estimated by applying multimode resonant cavity theory and a straight forward worst case approach. The results show that exceeding the International Commission on Non-Ionizing Radiation Protection (ICNIRP)guidelines due to simultaneous use of several mobile phones in enclosed areas is highly improbable.
Do elevators increase radiation from cell phone use?
Technically yes... But (according to ref 4) even at the worst cases, the simulation didn't reach the limits. But.... this is said at the last paragraph:
"However, the level of exposure greatly depends on the design of mobile phone. If the SAR produced by the mobile phone in the free space is already close to the limit, people will probably be exposed to an unacceptable level of RF radiation inside the metallic enclosed elevator. In addition, the SAR value could be greatly altered for different mobile phone positions and elevator dimensions. Therefore, further studies are required to clarify the RF human safety concern inside the en-closed metallic elevator."
TD;DR: Do elevators increase radiation from cell phone use?
Well, slightly, it may. However it's improbable that would in a harmful way according to Reference 4 and 5.