"Есть" has many functions and meanings. In the sense of "is", "are" it is omitted normally in the present tense.

In your example construction "У XXX есть YYY" means "XXX has YYY". It is different situation. Here есть also sometimes can be omitted but it can change the sense.

У тебя красивые глаза? - Are your eyes beautiful?
У тебя есть красивые глаза? - Do you have beautiful eyes?

Here usage of есть indicates that the idea of possession ("has") is logically emphasized. If есть is omitted, emphasis is on another idea.

У меня есть гвоздь. - I do have a nail.
У меня гвоздь. - A nail is what I have.
Гвоздь у меня. - It is me who has a nail.