There's a meta header you can set in your HTML to indicate whether a web site should run in full screen mode when running on an iphone.

<meta name="apple-mobile-web-app-capable" content="yes">

The documentation says:

If content is set to yes, the web application runs in full-screen mode; otherwise, it does not. The default behavior is to use Safari to display web content. You can determine whether a webpage is displayed in full-screen mode using the window.navigator.standalone read-only Boolean JavaScript property.

Found at http://developer.apple.com/safari/library/documentation/AppleApplications/Reference/SafariHTMLRef/Articles/MetaTags.html