Co-Founder & Head of R&D @Hachiko.
In the last decade I've been focusing on building teams and make them ship product in time.
After building several mobile web application I can say that the 3 top most common, mature, extensive and supported frameworks are:
Twitter Bootstrap: http://getbootstrap.com/
Zurb Foundation: http://foundation.zurb.com/
They are all "mobile first" and support all devices incl. desktop. they are responsive and you can really build an app on top of them.
Which one to pick you ask?
It really depends on the nature of you app.
for example, If you're focusing on parent child relationship and want to achieve nice page navigation of master-details, my gut feeling would probably go for jquery.mobile (page navigation: http://view.jquerymobile.com/1.3.2/dist/demos/widgets/transitions/)
For a heavy data entry app, bootstrap and zurb may be a better fit.
I'll be glad to hear more about your app and recommend the perfect fit for you.