Are you going to have anything between the kitchen and LR, such as an island? I think some kind of physical distinction would help.

I don't know if this is what you have in mind, but I'm posting in case the visuals help.

In this picture the coffers extend through to the kitchen, but the beam that runs above and parallel to the island could be a stopping point: so imagine beams on the LR side and not on the kitchen side.
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This one has an island with vertical cabs between the kitchen and FR. Beams on the FR ceiling and looks like no beams on the kitchen ceiling.
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In both of these examples a beam or soffit between the two spaces acts as a transition from one space to the next.

HTH

But both the pics have beams and pillars or some kind of support, we do not have that.
Do you think if we add fake beam or drop wall from celing we need to do pillars on either side to give a distinction.
Or an island (which we have ) is enough and we can have tray celing in the kitchen and coffered celing in the living.

So the options
1. Fake beam
2 drop wall supported by pillars on both side
3 tray ceiling in kitchen and coffered in living, do you guys think tray celing in the kitchen would look good.?

Open plans ARE a single room. Treat it as such. Do the ceiling as you would the floor. Use all one material/treatment for the whole space. Use other architectural elements to achieve separation of spaces. Or build walls so you don't have an open plan. If you are having a hard time visualizing the possibilities, then get your architect involved. He should have already offered some suggestions.

I love using ceiling variation to define areas. This photo shows how it can be done without beams or columns.

Coffered in the living room and tray in the kitchen....hmm....I think you would need visual separation of the two areas to make it work. Something like a partial wall with columns.

In this picture, they did a coffer with no dividing pillars. I think it looks a bit odd, but not bad...

beagles -- Thanks for posting that. It illustrates what NOT to do. That looks like a display area in a kitchen design shop. I agree with hollysprings; don't see a way to change ceilings unless you build some vertical visual dividers between the 'rooms'.

OP -- First, how much height are you working with? Do you have enough for coffering without making it feel oppressive? What size rooms are we talking about here?

I'm inclined to agree chisue- I sure wouldn't do it... but hopefully whomever's kitchen picture that is that I found on google likes it! :)

Thanks guys, very helpful advice.
My celing height is 9ft, with all the advice here, I think I am leaning towards making a drop wall with 2 pillars on either side . One near on the corner of stairs and the other at the other end.
You think it will look good?
Also i think I should do coffered in living and plain in kitchen as tray would interfere with cabinets and might look weird.

I would not do a coffered ceiling on a 9 foot ceiling. It will bring your ceiling height down too low I think. I think you need 10 feet minimum to do a pretty coffered ceiling. I would try to get the architectural detail in in another way, personally.

I definitely wouldn't do a coffered and a tray ceiling in what is essentially a large room. I associate tray ceilings with bedrooms though. . .